April 20, 2014
Hot Topics:
RSS RSS feed Download our iPhone app

The Recursive Filtering Workbench in Java, Putting it all Together

  • February 27, 2007
  • By Richard G. Baldwin
  • Send Email »
  • More Articles »

Java Programming Notes # 1513


Preface

This is the last installment of a multi-part tutorial on digital recursive filtering.  The first installment was published in the tutorial lesson entitled A Recursive Filtering Workbench in Java.  The second installment was published in the lesson entitled The Driver Class for the Recursive Filtering Workbench in Java.  The third installment was published in the lesson entitled The User Input GUI for the Recursive Filtering Workbench in Java.

The primary purpose of this lesson is to present and explain the Java code required to implement the interactive z-plane user interface shown in the top center of Figure 1 (and also shown in Figure 2).  A second purpose is to present and explain an inner class that cross-links the input GUI shown in the top right corner of Figure 1 with the interactive z-plane user interface.

This lesson builds on the information provided in the earlier lessons.  I won't repeat much of the information from those earlier lessons here.  Unless you are already well-schooled in digital recursive filtering, it will probably be a good idea for you to study the earlier lessons before embarking on this lesson.

A Recursive Filtering Workbench

The complete collection of four installments presents and explains the code for an interactive Recursive Filtering Workbench (See Figure 1) that can be used to design, experiment with, and evaluate the behavior of digital recursive filters.

By the end of this installment, you should have learned how to write a Java program to create such an interactive workbench.  Hopefully, you will also have gained some understanding of what recursive filters are, how they behave, and how they fit into the larger overall technology of Digital Signal Processing (DSP).

Viewing tip

You may find it useful to open another copy of this lesson in a separate browser window.  That will make it easier for you to scroll back and forth among the different listings and figures while you are reading about them.

Supplementary material

I recommend that you also study the other lessons in my extensive collection of online Java tutorials.  You will find those lessons published at Gamelan.com.  However, as of the date of this writing, Gamelan doesn't maintain a consolidated index of my Java tutorial lessons, and sometimes they are difficult to locate there.  You will find a consolidated index at www.DickBaldwin.com.

I also recommend that you pay particular attention to the lessons listed in the References section of this document.

Preview

Figure 1 shows a full screen shot of the workbench in operation.


Figure 1

In order to accommodate this narrow publication format, the screen shot in Figure 1 was reduced to the point that the individual images are no longer legible.  The purpose of Figure 1 is to provide an overview of the workbench.  That overview will be used in conjunctions with references in the paragraphs that follow.  (Full-size versions of the individual images from Figure 1 will be presented later.)

Complex poles and zeros

The workbench makes it possible for the user to design a recursive filter by specifying the locations of sixteen poles and sixteen zeros in the complex z-plane and then to evaluate the behavior of the recursive filter for that set of poles and zeros.  The user can relocate the poles and zeros and re-evaluate the behavior of the corresponding recursive filter as many times as may be useful without a requirement to restart the program.

An image of the z-plane

The GUI in the top center portion of the screen in Figure 1 is an image of the complex z-plane showing the unit circle along with the locations of all the poles and zeros.

(Because of the reduction in the size of the image, the poles and zeros are only barely visible in Figure 1.  A full-size version is shown in Figure 2.)


Figure 2

The user can interactively change the location of any pair of complex poles or zeros by selecting a specific pair of poles or zeros with the radio buttons in Figure 3 and clicking the new location with the mouse in the z-plane GUI.  This provides a quick and easy way to position the poles and zeros in the z-plane.

Numeric text input

The GUI that is partially showing in the upper right corner of Figure 1 contains four text fields and a radio button for each pair of complex poles and each pair of complex zeros.  (A full-size version of this GUI is shown in Figure 3.)


Figure 3

Purpose of this GUI

This GUI has several purposes.  For example, the user can specify the locations of pairs of poles or zeros very accurately by entering the real and imaginary coordinate values corresponding to the locations into the text fields in this GUI.  The user can also view the length and the angle (relative to the real axis) of an imaginary vector that connects each pole and each zero to the origin.

This GUI also provides some other features that are used to control the behavior of the workbench program.

The two GUIs are connected

When this GUI is used to relocate a complex pair of poles or zeros, the graphical image of the z-plane in Figure 2 is automatically updated to reflect the new location.  Similarly, when the mouse is used with the graphical image of the z-plane in Figure 2 to relocate a pair of poles or zeros, the numeric information in the GUI in Figure 3 is automatically updated to reflect the new location. 

Two ways to specify the location of poles and zeros

Thus, these two GUIs working together provide two different ways that the user can specify the locations of poles and zeros.  Clicking the location with the mouse in the z-plane is very quick and easy but not particularly accurate.  Entering the numeric coordinate values into the text fields takes a little more effort, but is very accurate.

The two approaches can be used in combination to create a rough design with the mouse and then to polish the design by entering accurate pole and zero locations into the text fields.

The behavior of the recursive filter

Once the locations of the poles and zeros that define a recursive filter have been established using either or both of the two GUIs discussed above, the leftmost GUI in Figure 1 can be used to display the following information about the recursive filter.  (See Figure 4 for a full-size version of this GUI.)

  • The impulse response in the time domain.
  • The amplitude response in the frequency domain.
  • The phase response in the frequency domain.


Figure 4

Two computational approaches

Two versions of the amplitude response and two versions of the phase response are plotted in the GUI shown in Figure 4.  One version is based on the Fourier Transform of the impulse response.  The other version is based on a vector analysis of the locations of the poles and zeros in the z-plane.

Adjusting the plotting parameters

The GUI shown in Figure 4 provides for the input of seven different plotting parameters (vertical scale, horizontal scale, tic mark locations, etc.).  The user can modify the plotting parameters and replot the graphs as many times as may be useful to get a good visual representation of the behavior of the recursive filter.

General Background Information

I will not attempt to teach you the theory behind recursive filtering in this multi-part tutorial.  Rather, I will assume that you already understand that theory, or that you are studying a good theoretical resource on recursive filtering concurrently with the study of this lesson.

(A very good resource on the theory of digital filtering in general, and recursive digital filtering in particular, is the Introduction to Digital Filters with Audio Applications by Julius O. Smith III .)

See the earlier lesson entitled A Recursive Filtering Workbench in Java for general background information on recursive filtering in general and this recursive filtering workbench in particular.

Discussion and Sample Code

This program is composed of several rather long classes, resulting in a large program.  The size of the program is the main reason that I am publishing it in several installments.  This final installment will present and explain the code in two inner classes:

  • MyTextListener
  • ZPlane

The inner class named MyTextListener supports the code required to implement the GUI shown in the upper right corner of Figure 1, and also serves to cross-link that GUI with the interactive z-plane GUI shown in the top center of Figure 1.

The inner class named ZPlane is responsible for almost all aspects of the interactive z-plane GUI shown in the top center of Figure 1.

I will begin my explanation with the inner class named MyTextListener.

MyTextListener Class

This is an inner TextListener class.  An object of this class is registered on all of the text fields containing coordinate data in Figure 3, and is notified whenever the text value for any of the real or imaginary values in the pole and zero text fields changes for any reason.

When the event handler is notified that a TextEvent has occurred, it computes and displays the angle specified by the ratio of the imaginary part to the real part (see Figure 3).  All angles are expressed in degrees between 0 and 359.9 inclusive.

Also, when notified that an event has occurred, the event handler computes and displays the length of an imaginary vector connecting the pole or zero to the origin as the square root of the sum of the squares of the real and imaginary parts.

Finally, when notified of a TextEvent, (which indicates that there has been a change in a real or imaginary coordinate value of a pole or zero), the event handler causes the z-plane to be repainted in order to display the new location for the pole or zero represented by the text field that fired the event.  Therefore, the z-plane is repainted whenever there is a change in the contents of any of the text fields containing pole or zero coordinate data.

The textValueChanged method

The event handling method for a TextEvent is the method named textValueChangedListing 1 shows the beginning of the inner class named MyTextListener and the beginning of the method named textValueChanged.

class MyTextListener implements TextListener{
  
  public void textValueChanged(TextEvent e){
    captureTextFieldData();

Listing 1

The code in Listing 1 invokes the method named captureTextFieldData to cause the latest values in the text fields to be converted to numeric double values and stored in arrays.  I explained the method named captureTextFieldData in an earlier lesson.

Description of the process

Listing 2 shows the beginning of code that will identify the text field that fired the event and respond appropriately by taking the actions described earlier.  In addition to those actions described earlier, the state of the radio button associated with the modified text field will be set to selected.

The basic process is to get the value of the name property of the text field that fired the event and to compare that value with the previously known name property values of each of the text fields containing coordinate data until a match is found.  For example, the text fields containing pole coordinate values are known to have names such as the following:

  • poleReal0
  • poleReal6
  • poleImag3
  • poleImag5

This information can be used to quickly identify the text field that fired the event.

First, a for loop is used to test for a match with the text fields containing coordinate data for the poles.  If a match is found within that set of text fields, a flag named firingObjFound is set to prevent the searching of the text fields containing coordinate data for the zeros, the appropriate actions are taken, and control breaks out of the loop.

If no match is found for the poles, a different for loop is used to search the text fields containing coordinate data for the zeros.  When the match is found, the appropriate actions are taken, and control breaks out of that loop.

Identify the source of the event

Listing 2 sets the value of firingObjFound to false in preparation for entering the first for loop.  Then Listing 2 uses the reference to the source object obtained as a parameter to the event handler method to get and save the value of the name property of the text field that fired the event.

    boolean firingObjFound = false;

    String name = ((Component)e.getSource()).getName();

Listing 2

Search the poles

The for loop that is used to search the text fields containing coordinate values for the poles is shown in Listing 3.

    for(int cnt = 0;cnt < numberPoles/2;cnt++){
      if((name.equals("poleReal" + cnt)) || 
                          (name.equals("poleImag" + cnt))){

        //Compute and set the angle to the pole.
        poleAngle[cnt].setText(getAngle(
                     poleRealData[cnt],poleImagData[cnt]));

        //Compute and set the length of an imaginary vector
        // connecting the pole to the origin.
        poleLength[cnt].setText("" + sqrt(
                     poleRealData[cnt]*poleRealData[cnt] +
                     poleImagData[cnt]*poleImagData[cnt]));

        //Select the radio button.
        poleRadioButtons[cnt].setSelected(true);

        firingObjFound = true;//Avoid testing zeros

        break;
      }//end if
    }//end for loop

Listing 3

Compute and display the angle

The code in Listing 3 begins by testing the value of the name property of the text field that fired the event against the known name property values of the text fields containing real and imaginary coordinate values for the poles.  If the value of the name property of the text field that fired the event matches the known value for one of the text fields containing coordinate data for a pole, the getAngle method is called to return the value for the angle shown in the Angle column in Figure 3.  That value is set into the appropriate text field in that column.  (I will explain the getAngle method shortly.)

Compute and display the vector length

Then the code in the for loop in Listing 3 calls the sqrt method of the Math class to compute the length of an imaginary vector connecting the pole to the origin.  The length of the vector is then set into the appropriate text field in the Length column in Figure 3.

(Note that when the sqrt method is called, it is not qualified by the name of the class.  This is because a static import directive was used for the Math class.  This only works for Java version 1.5 or later.)

Select the corresponding radio button

Then the code in the for loop in Listing 3 sets the selected property value for the pole whose coordinate value has changed to true.

Set the flag and break out of the loop

Finally the code in the for loop sets the value of the flag named firingObjFound to true, and breaks out of the for loop without testing any other text fields (beyond the text fields for which the match was found)

As you will see, setting the value of the flag named firingObjFound to true prevents the code from searching the text fields containing zero coordinate data seeking a match, because the matching text field has already been identified and processed.

If a match is not found by the first for loop...

If a match is not found in the for loop in Listing 3, control exits that for loop with the value of the flag named firingObjFound still set to false because it was set to false in Listing 2 and was not modified in Listing 3.

The code in Listing 4 begins by testing the value of the flag.  If it is true, this means that the text field that fired the event has already been identified and processed and all of the remaining code in Listing 4 is skipped.

If the flag is false, the for loop in Listing 4 is processed to identify and process the text field containing zero coordinate data in a manner that is essentially the same as that described above.

    if(!firingObjFound){
      for(int cnt = 0;cnt < numberZeros/2;cnt++){
        if((name.equals("zeroReal" + cnt)) || 
                          (name.equals("zeroImag" + cnt))){
          //Compute and set the angle to the zero.
          zeroAngle[cnt].setText(getAngle(
                     zeroRealData[cnt],zeroImagData[cnt]));
          //Compute and set the length of an imaginary
          // vector connecting the zero to the origin.
          zeroLength[cnt].setText("" + sqrt(
                     zeroRealData[cnt]*zeroRealData[cnt] +
                     zeroImagData[cnt]*zeroImagData[cnt]));
          //Select the radio button.
          zeroRadioButtons[cnt].setSelected(true);
          break;
        }//end if
      }//end for loop
    }//end if on firingObjFound

Listing 4

Because an event was fired by one of the text fields containing coordinate data for the poles and zeros, and because the poles have already been ruled out, a match will be found in Listing 4 for one of the text fields containing coordinate data for one of the zeros.  When that text field is identified and processed, control will break out of the for loop without examining the remaining text fields for a match.

Repaint the z-plane

Regardless of which text field fired the event, the event handling code in Listing 5 calls the repaint method on the z-plane object causing all of the poles and zeros to be redrawn, including the one that was being relocated when the event was fired.

    refToZPlane.repaint();
    
  }//end textValueChanged

Listing 5

Initial concerns about responsiveness

Note that each character that you type into the text field causes a TextEvent to be fired.  Each time an event is fired, the repaint method is called on the z-plane object.  Initially I was concerned that this may overburden the system by causing a series of calls to the repaint method to be made in quick succession. 

Doesn't seem to be a problem

However, my old and rather slow laptop computer doesn't have any problem handling this.  I believe that is probably because the system doesn't try to respond to all of the calls to the repaint method if they are being received at a faster rate than can be accommodated.  I believe that when that happens, only the latest call to the repaint method is honored.  This prevents the painting of scenes that wouldn't be visible long enough to be viewed anyway.

The method named getAngle

The method named getAngle is called in Listing 3 and Listing 4 to determine the angle (relative to the real or horizontal axis) described by an imaginary vector that connects a pole or a zero to the origin.  This method receives the real and imaginary coordinates of a point in the complex z-plane and returns the angle described by that point in the range from 0 to 359.9 degrees as type String suitable for storing in a text field.

The method begins in Listing 6.

  String getAngle(double realVal,double imagVal){
    String result = "";
    //Avoid division by 0
    if((realVal == 0.0) && (imagVal >= 0.0)){
      result = "" + 90;
    }else if((realVal == 0.0) && (imagVal < 0.0)){
      result = "" + 270;

Listing 6

Handle some unique cases

The code in Listing 6 tests first to determine if the value of the real coordinate is zero.  If so, there is no need to compute the angle, because it is known to be either 90 degrees or 270 degrees.  Some logic is executed to determine which is the correct answer and that value is returned.

The general case

However, if the value of the real coordinate is not zero, it is necessary to compute the angle.  The code to accomplish that begins in Listing 7.

    }else{
      //Compute the angle in radians.
      double angle = atan(imagVal/realVal);

      //Adjust for negative coordinates
      if((realVal < 0) && (imagVal == 0.0)){
        angle = PI;
      }else if((realVal < 0) && (imagVal > 0)){
        angle = PI + angle;
      }else if((realVal < 0) && (imagVal < 0)){
        angle = PI + angle;
      }else if((realVal > 0) && (imagVal < 0)){
        angle = 2*PI + angle;
      }//end else

Listing 7

Call the arc tangent method

The code in Listing 7 calls the arc tangent (atan) method of the Math class to compute and return the angle in radians.  There is an ambiguity with this approach, however.  The value of the actual angle can be any angle from 0 to 2*PI.  However, the atan method returns the angle normalized to the range from negative PI/2 to PI/2.  We still don't know the actual angle if the point is in the second or third quadrants of the z-plane.

After the angle is obtained in Listing 7, some logic is performed on the coordinate values to adjust the angle, causing it to reflect the correct quadrant.

Convert from radians to degrees

The statement in Listing 8 converts the angle from radians to degrees.

      angle = angle*180/PI;

Listing 8

Convert to type String

The code in Listing 9 converts the angle from type double to type String suitable for storing in a TextField object.

      String temp1 = "" + angle;

      if(temp1.length() >= 5){
        result = temp1.substring(0,5);
      }else{
        result = temp1;
      }//end else
    }//end else
    return result;
  }//end getAngle
  //-----------------------------------------------------//

}//end inner class MyTextListener

Listing 9

There is another item to be dealt with and that is the number of digits in the string representation of the angle.  A simple conversion of the angle from type double to type String can result in a large number of significant digits.  However, since the string is being generated solely for human consumption, displaying a large number of significant digits for the angle may not be useful.

The code in Listing 9 takes this into account by discarding all characters beyond the fifth character in the string representation of the angle

End of the class

Listing 9 also signals the end of the class definition for the class named MyTextListener.  That concludes my explanation of the inner class named MyTextListener.  I will begin the explanation of the inner class named ZPlane in the next section.

ZPlane Class

The purpose of this inner class is to provide the graphical z-plane interface shown in Listing 2.

A brief review on Java graphics

Before getting into the details of the class, I will provide a brief review of how you cause a drawing to be rendered inside an object of type Frame on the computer screen.  This review will be brief and will skip many important details.  If you would like to learn more about this topic, I have published many tutorial lessons on my web site that address the topic in detail.

Override the paint method

You begin by overriding an inherited method named paint.  The paint method always receives a reference to an object of either type Graphics, or type Graphics2D, which is a subclass of Graphics.

Although this is something of an oversimplification, you can think of that object as representing a drawing surface on the portion of the computer screen occupied by the Frame.

Change the colors of the pixels

To cause a drawing or an image to appear on the screen, you need to cause the colors of selected pixels to be different from the colors of the pixels that surround them.  For example, for a simple line drawing, you may elect to represent the lines as black pixels on a background of white pixels.  For a photograph-style image, you need to cause the colors of the selected pixels to represent the various colors in the image.

Many methods available

The code in the overridden paint method can use any of a large number of methods defined in the Graphics and Graphics2D classes to control the colors of selected pixels.  It is through control over the colors of the pixels that you turn your idea into an image that may be viewed and (hopefully) appreciated by a human consumer.

When the screen needs to be repainted...

Whenever the screen space occupied by the Frame needs to be repainted, the Java virtual machine, and ultimately the operating system will cause your overridden paint method to be executed, at which time the code that you have written will exercise control over the colors of the pixels in that area on the screen.

There are many things that can create a need for repainting the area of the screen occupied by the Frame.  For example, the user may cover the Frame with some other application, and then uncover it.

Purposely repainting the screen

Sometimes the code in the program decides that it is time to cause the screen to be repainted.  In this case, the program will invoke the repaint method on a reference to the Frame object.  This should be viewed as a request (not a command) to the operating system to cause the area occupied by the Frame to be repainted.  If the operating system honors the request, several things will happen in sequence, but eventually the overridden paint method will be executed, causing that portion of the screen to be repainted.

Beginning of the class named ZPlane

Now I will explain the class named ZPlane.  The class definition begins in Listing 10 with the declaration of several instance variables and the initialization of some of them.

class ZPlane extends Frame{
  Insets insets;
  int totalWidth;
  int totalHeight;
  //Set the size of the display area in pixels.
  int workingWidth = 464;
  int workingHeight = 464;
  int unitCircleRadius = 200;//Radius in pixels.
  int translateOffsetHoriz;
  int translateOffsetVert;

Listing 10

Note that the class extends the class named Frame, thereby causing the brief explanation on graphics that I provided earlier to apply directly to an object of this class.

(The ability to draw images in Java is not limited to the use of Frame objects.  The repaint method and a default version of the paint method are defined in and inherited from the Component class.  Therefore, it should be possible to override the paint method in the definition of any class that extends the Component class and then to invoke the repaint method on a reference to that object.)

The constructor

The constructor code for the class named ZPlane begins in Listing 11.

  ZPlane(){//constructor
    setVisible(true);
    insets = getInsets();
    setVisible(false);

    totalWidth = workingWidth + insets.left + insets.right;
    totalHeight = 
                workingHeight + insets.top + insets.bottom;

    setTitle("Copyright 2006, R.G.Baldwin");

Listing 11

The code in Listing 11 gets and saves the sizes of the borders and the banner on the Frame object.  Those sizes can be gotten through the invocation of the getInsets method on a reference to the Frame, but only while the Frame is visible.  Therefore, the code in Listing 11 makes the Frame visible just long enough to get those values.  (The frame is ultimately made visible for the long term by code in the InputGUI class.)

Set total width and height values for the frame

The code in Listing 11 uses those inset values to compute and set the values in the variables named totalWidth and totalHeight.  These two variables will be used later to set the overall size of the display so as to accommodate the insets and still provide a display area whose size is specified by the values stored in workingWidth and workingHeight.  These working values were established when the variables were declared and initialized in Listing 10.

Finally the code in Listing 11 sets the title in the banner at the top of the z-plane object as shown in Figure 2.

Set the size and the location of the display

Listing 12 invokes the setBounds method to establish the size and the location of the display.  The size is set to the totalWidth and totalHeight values that were computed in Listing 11.  This causes the display to have a working area that is specified by the initial values of workingWidth and workingHeight.

Elsewhere in the program, the resizable property of the display is set to false so that the user cannot modify the size.

The first two parameters to the setBounds method in Listing 12 cause the display to be located in the upper-center of the screen as shown in Figure 1.

    setBounds(408,0,totalWidth,totalHeight);

Listing 12

Prepare to move the plotting origin

By default, the plotting origin is at the upper left corner of the Frame, outside the left border and outside the top banner.  Listing 13 computes two values that will be used elsewhere in the program to effectively move the origin to the center of the working area.

Note, however, that the direction of positive-y is down the screen instead of up the screen as is the customary direction of positive-y when plotting.  This is compensated for elsewhere in the program.

    translateOffsetHoriz = workingWidth/2 + insets.left;
    translateOffsetVert = workingHeight/2 + insets.top;

Listing 13

(As an aside, I will mention that I may have been able to eliminate some of the complexity in the above code involving insets if I had placed a Canvas object in the CENTER of the Frame and had drawn my pictures on the canvas.  However, it still would have been necessary for me to deal with insets in order to set the overall size of the Frame for a specified size of the working area.  This is because the inset values vary from one look-and-feel to the next.)

Condition the close button

Listing 14 registers a window listener that terminates the program when the user clicks the X-button in the upper right corner of the frame.

    addWindowListener(
      new WindowAdapter(){
        public void windowClosing(WindowEvent e){
          System.exit(0);//terminate the program
        }//end windowClosing
      }//end class def
    );//end addWindowListener
  }//end constructor

Listing 14

Listing 14 also signals the end of the constructor for the ZPlane class.

Override the paint method

Listing 15 shows the beginning of the overridden paint method.

  public void paint(Graphics g){
    //Translate the origin to the center of the working
    // area in the frame.
    g.translate(translateOffsetHoriz,translateOffsetVert);

    //Draw a round oval to represent the unit circle in the
    // z-plane.
    g.drawOval(-unitCircleRadius,-unitCircleRadius,
               2*unitCircleRadius,2*unitCircleRadius);

    //Draw horizontal and vertical axes at the new origin.
    g.drawLine(-workingWidth/2,0,workingWidth/2,0);
    g.drawLine(0,-workingHeight/2,0,workingHeight/2);

Listing 15

The code in Listing 15 is straightforward and shouldn't require an explanation beyond that contained in the embedded comments.  I suggest that you view Figure 2 while studying the code in Listing 15 so that you can correlate the code with the features in the display.

Get the latest coordinate values

Listing 16 invokes the captureTextFieldData method to cause the latest data in the text fields in Figure 3 to be converted to double numeric values and stored in arrays suitable for use in plotting the pole and zero locations.

    captureTextFieldData();

Listing 16

It doesn't matter how the coordinate values were placed in the text fields.  They may have been placed there by code executing elsewhere in the program.  They may have been placed there by the user manually typing the values into the text fields.  The overridden paint method doesn't care.  When the paint method is executed, the latest coordinate values stored in those text fields are converted from string values to numeric values and used to draw the poles and the zeros in their current locations.

Draw the poles as small red squares

The code in Listing 17 draws each pole whose location is given in Figure 3, and its complex conjugate, as a small red square (four pixels on each side) using coordinate information extracted from the text fields by the method call in Listing 16.  The square is centered on the specified location of the pole.

Note that the value of unitCircleRadius in pixels is used to convert the coordinates of the poles from double values to screen pixels.

    g.setColor(Color.RED);
    
    for(int cnt = 0;cnt < poleRealData.length;cnt++){
      //Compute the coordinates in pixels.
      int realInt = 
                 (int)(poleRealData[cnt]*unitCircleRadius);
      int imagInt = 
                 (int)(poleImagData[cnt]*unitCircleRadius);

      //Draw the pair of complex conjugate poles.
      g.drawRect(realInt-2,imagInt-2,4,4);
      g.drawRect(realInt-2,-imagInt-2,4,4);
    }//end for loop

Listing 17

(Note the sign conversion on the imaginary coordinate value used to draw the conjugate pole.)

Although it isn't obvious in Figure 2, each time this overridden paint method is executed, all sixteen poles are drawn.  In Figure 2, two poles that comprise one complex conjugate pair are stacked on top of one another on the real axis just inside the unit circle.  The remaining fourteen poles are all stacked on top of one another at the origin.

Draw the zeros as small black circles

Listing 18 draws each zero as a small black circle with a diameter of four pixels.  Except for the fact that the code in Listing 18 draws black ovals instead of red rectangles, the code in Listing 18 is essentially the same as the code in Listing 17.

    g.setColor(Color.BLACK);//Restore color to black
    
    for(int cnt = 0;cnt < zeroRealData.length;cnt++){
      //Draw the conjugate pair of zeros as small black
      // circles centered on the zeros.
      int realInt = 
                 (int)(zeroRealData[cnt]*unitCircleRadius);
      int imagInt = 
                 (int)(zeroImagData[cnt]*unitCircleRadius);
      //Draw the pair of conjugate zeros.
      g.drawOval(realInt-2,imagInt-2,4,4);
      g.drawOval(realInt-2,-imagInt-2,4,4);
    }//end for loop

  }//end overridden paint method
}//end inner class ZPlane

Listing 18

In Figure 2, two zeros that constitute one complex conjugate pair are drawn on the unit circle at about ten to fifteen degrees off the horizontal.  All fourteen of the remaining zeros are stacked (along with the poles) at the origin.

End of paint method and end of ZPlane class

Listing 18 also signals the end of the overridden paint method and the end of the inner class named ZPlane.  Therefore, that concludes my explanation of the class named ZPlane.

In the next section, I will summarize how the event handlers in the various classes in this program work together to make it interactive.

Interactive Summary

This program exhibits two interesting areas of interactive behavior.  One interesting area has to do with the user interface shown in Figure 4.  The other interesting area has to do with the combination of the user interfaces shown in Figure 2 and Figure 3.

Interactive plotting

The main interactive feature that is interesting about Figure 4 is that there is no (practical) limit to how many times the user can change any of the seven plotting parameters in the text fields at the bottom of Figure 4 and cause the plots to be re-generated and re-displayed by clicking the Graph button without a requirement to restart the program.

However, although this is the first time that I have used this capability to evaluate recursive filtering, I have been using the general capability exhibited by Figure 4 for several years.  I'm certain that I have explained how it works in more than one of my earlier online tutorials.  Therefore, I'm not going to bore you by explaining it again.

You can refer to the links in the References section to find some of those earlier tutorial lessons, or you can do a Google search using one or the other of the following sets of keywords to locate my previously published tutorial lessons that use this capability

  • baldwin java Graph03
  • baldwin java GraphIntfc01

Moving poles and zeros

I will concentrate on the interactive feature that has to do with the combination of the user interfaces shown in Figure 2 and Figure 3 for the remainder of this section.

Very early in this installment, I told you that the two GUIs are connected.  When the GUI shown in Figure 3 is used to relocate a complex pair of poles or zeros by manually typing new coordinates into the text fields, the graphical image of the z-plane in Figure 2 is automatically updated to reflect the new location.  Similarly, when the mouse is used with the graphical image of the z-plane in Figure 2 to relocate a pair of poles or zeros, the numeric information in the GUI in Figure 3 is automatically updated to reflect the new location.

A mouse listener on the z-plane

As you learned in an earlier installment of this multi-part tutorial, code in the InputGUI class defines and registers a mouse listener on the z-plane object.  When the user selects a specific pair of poles or zeros by selecting a radio button in Figure 3 and then uses the mouse to click somewhere in the z-plane in Figure 2, the mouse listener is notified of a MouseEvent.

(Actually, because one of the radio buttons is always selected, any time that the user clicks in the z-plane, the mouse listener will be notified even if the user neglects to select a specific pair of poles or zeros in advance.)

Get and save the coordinates of the mouse click

The event handler uses the incoming MouseEvent object to determine the coordinates of the mouse click in the z-plane.  Believing that the user desires to relocate the selected pole or zero to the position specified by those coordinates, the mouse listener converts the coordinates to string values and stores them in the text fields for the selected pole or zero in the Real and Imag columns of Figure 3.

A TextEvent is fired

As you learned earlier in this installment, when the contents of a text field containing coordinate data change, that text field fires one or more text events.  An object of the MyTextListener class was registered to listen for text events on all of the text fields in Figure 3 that contain real or imaginary coordinate data for the poles and zeros.

Behavior of the TextEvent handler

As explained earlier, the TextEvent handler performs several actions (such as computing and displaying the angle and the length of the vector) and also invokes the repaint method on the reference to the z-plane object.

As I explained in the explanation of the ZPlane class, this causes the overridden version of the paint method for that class to be executed.  The overridden version of the paint method gets the latest coordinate data from the text fields in Figure 3 and uses that data to repaint the z-plane (see Figure 2) showing all of the poles and zeros in their most current locations.  This includes the poles or zeros that have been relocated to the location of the most recent mouse click in the z-plane.

What about the manual entry of coordinate values?

That explains how both Figure 2 and Figure 3 get updated when the user clicks the mouse somewhere in the z-plane display.  What happens if the user simply types a new coordinate value into a text field in Figure 3?  The situation is somewhat simpler in this case.  The physical act of typing the new coordinate value into the text field causes the text field in Figure 3 to be automatically updated.  Regardless of what causes the text values in the text field to change, whenever that happens:

  • The text field fires one or more text events
  • The registered TextEvent handler gets notified of each event
  • The TextEvent handler invokes the repaint method on the z-plane, causing the overridden paint method to be executed
  • The overridden paint method gets the latest coordinate values from the text fields (including the most recent changes)
  • The overridden paint method repaints the display reflecting the latest positions for the poles and the zeros

Like the keystone an arch...

Therefore, like the keystone in an arch, the MouseEvent handler in the InputGUI class, the TextEvent handler in the MyTextListener class, and the overridden paint method in the ZPlane class work together, (and work with all the other code in the program) to form the keystone of the interactive recursive filtering workbench.

Run the Program

I encourage you to copy the code from Listing 19 into your text editor, compile it, and execute it.  Experiment with it, making changes, and observing the results of your changes.

Remember that in addition to the code from Listing 19, this workbench program requires access to the following source code or class files, which were published in earlier tutorials (see the References section of this document for links to those lessons):

  • GraphIntfc01
  • ForwardRealToComplexFFT01
  • Graph03

(You can also find the source code for these classes by searching for the class names along with the keywords baldwin java on Google.)

Having compiled all the source code, enter the following command at the command prompt to run this program:

java Graph03 Dsp046

Summary

The earlier tutorial lesson entitled A Recursive Filtering Workbench in Java was the first installment of a multi-part tutorial on recursive filtering.  That lesson provided an overview of an interactive Recursive Filtering Workbench that can be used to design, experiment with, and evaluate the behavior of digital recursive filters.

The second installment, entitled The Driver Class for the Recursive Filtering Workbench in Java, presented and explained the driver class for the workbench. (The driver class is named Dsp046.)

This third installment entitled The User Input GUI for the Recursive Filtering Workbench in Java presented and explained the class named InputGUI, from which one of three major GUIs is constructed.  The GUI constructed from the InputGUI class, (which is shown in the upper right corner of Figure 1), deals mainly with text input and text output. 

A second GUI, shown in the upper left corner of Figure 1 deals mainly with the presentation of graphic data to the user.  It was explained in the second installment. 

The third GUI, shown in the top center of Figure 1 deals mainly with mouse input and program output in a graphic context.  The code for that GUI is explained in this, the fourth and final installment.

This final installment presents and explains the code in two inner classes:

  • MyTextListener
  • ZPlane

Like the keystone in an arch, the MouseEvent handler in the InputGUI class, the TextEvent handler in the MyTextListener class, and the overridden paint method in the ZPlane class work together, (and work with all the other code in the program) to form the keystone of the interactive recursive filtering workbench.

What's Next?

That wraps it up for this multipart tutorial.  At this time, I have no further plans to publish any additional tutorials on this topic.

References

An understanding of the material in the following previously published lessons will be very helpful to you in understanding the material in this lesson:

  • 1510 A Recursive Filtering Workbench in Java
  • 1511 The Driver Class for the Recursive Filtering Workbench in Java
  • 1512 The User Input GUI for the Recursive Filtering Workbench in Java
  • 1468 Plotting Engineering and Scientific Data using Java
  • 100   Periodic Motion and Sinusoids
  • 104   Sampled Time Series
  • 108   Averaging Time Series
  • 1478 Fun with Java, How and Why Spectral Analysis Works
  • 1482 Spectrum Analysis using Java, Sampling Frequency, Folding Frequency, and the FFT Algorithm
  • 1483 Spectrum Analysis using Java, Frequency Resolution versus Data Length
  • 1484 Spectrum Analysis using Java, Complex Spectrum and Phase Angle
  • 1485 Spectrum Analysis using Java, Forward and Inverse Transforms, Filtering in the Frequency Domain
  • 1486 Fun with Java, Understanding the Fast Fourier Transform (FFT) Algorithm
  • 1487 Convolution and Frequency Filtering in Java
  • 1488 Convolution and Matched Filtering in Java
  • 1492 Plotting Large Quantities of Data using Java
  • Other previously-published lessons on DSP including adaptive processing and image processing

In addition, there are numerous good references on DSP available on the web.  For example, good references can be found at the following URLs:

Complete Program Listing

Complete listings of the classes discussed in this lesson are contained in Listing 19 below.
 
/* File Dsp046.java
Copyright 2006, R.G.Baldwin

This program provides a visual, interactive recursive 
filtering workbench.

The purpose of the program is to make it easy to experiment
with the behavior of recursive filters and to visualize the
results of those experiments.

The program implements a recursive filter having eight 
pairs of complex conjugate poles and eight pairs of complex
conjugate zeros.  The locations of the pairs of poles and
zeros in the z-plane are controlled by the user.

Although the pairs of poles and zeros can be co-located on
the real axis, the program does not support the placement
of individual poles and zeros on the real axis.

The user can reduce the number of poles and zeros used by
the recursive filter by moving excess poles and zeros to 
the origin in the z-plane, rendering them ineffective in 
the behavior of the recursive filter.

The program provides three interactive displays on the 
screen.  The first display (in the leftmost position on the
screen) contains five graphs.  The first graph in this 
display shows the impulse response of the recursive filter 
in the time domain.  

The second and third graphs in the first display show the 
amplitude response of the recursive filter in the frequency
domain computed using two different approaches.  The two 
different computational approaches are provided for 
comparison purposes.

The first computational approach for computing the 
amplitude response is to perform a Fourier transform on
the impulse response using an FFT algorithm.  The quality
of the estimate of the amplitude response using this 
approach is dependent on the extent to which the entire
impulse response is captured in the set of samples used to
perform the FFT.  If the impulse response is truncated, the
estimate will be degraded.

The second approach for computing the amplitude response 
involves computing the product of the vector lengths from 
each point on the unit circle to each of the poles and each
of the zeros in the z-plane.  This approach provides an
idealized estimate of the amplitude response of the 
recursive filter, unaffected by impulse-response 
considerations.  This approach provides the same results 
that should be produced by performing the FFT on a set of
impulse-response samples of sufficient length to guarantee
that the values in the impulse response have been damped
down to zero (the impulse response is totally captured in
the set of samples on which the FFT is performed).

The fourth and fifth graphs in the first display show the 
phase response of the recursive filter computed using the 
same (or similar) approaches described above for the 
amplitude response.  (The second approach uses the sum of
vector angles instead of the product of vector lengths.)
Once again, the two approaches are provided for comparison
purposes.

By default, the program computes and captures the impulse 
response for a length of 1024 samples and performs the 
Fourier transform on that length.  However, the length of 
the captured impulse response and the corresponding FFT
can be changed by the user to any length between 2 samples
and 16384 samples, provided that the length is an even 
power of two.  (If the length specified by the user is not
an even power of two, it is automatically changed to an
even power of two by the program.)

The first display is interactive in the sense that there 
are seven different plotting parameters that can be 
adjusted by the user in order to produce plots that are 
visually useful in terms of the vertical scale, the 
horizontal scale, the location of tic marks, etc.  The
user can modify any of the parameters and then click a 
Graph button to have the graphs re-plotted using the new
parameters.

The second display (which appears in the upper center
of the screen) shows the locations of all of the poles and 
zeros in the z-plane.  The user can use the mouse to change
the location of any pair of complex conjgate poles or zeros
by first selecting a specific pair of poles or zeros and 
then clicking the new location in the z-plane.  This 
interactive capability makes it possible for the user to 
modify the design of the recursive filter in a completely
graphic manner by positioning the poles and zeros in the 
z-plane with the mouse.

Having relocated one or more pairs of poles or zeros in the
z-plane, the user can then click the Graph button in the 
first display described earlier to cause the new impulse 
response, the new amplitude response, and the new phase 
response of the new recursive filter with the modified pole
and zero locations to be computed and displayed.

The third display (that appears in the upper-right of the
screen) is a control panel that uses text fields, ordinary
buttons, and radio buttons to allow the user to perform the
following tasks.

1. Specify a new length for the impulse response as an even
power of two.  (Once again, if the user fails to specify an
even power of two, the value provided by the user is 
converted to an even power of two by the program.)

2. Cause all of the poles to be moved to the origin in the
z-plane.

3. Cause all of the zeros to be moved to the origin in the
z-plane.

4. Select a particular pair of complex conjugate poles or 
zeros to be relocated using the mouse in the display of the
z-plane.

5. View the angle described by each pole and zero relative
to the origin and the horizontal axis in the z-plane.

6. View the length of an imaginary vector that connects
each pole and zero to the origin.

7. Enter (into a text field) a new real or imaginary value
specifying the location of a pair of complex conjugate 
poles or zeros in the z-plane.

When a new real or imaginary value is entered, the angle 
and the length are automatically updated to reflect the new
location of the pole or zero and the display of the pole or
zero in the z-plane is also updated to show the new 
location.

Conversely, when the mouse is used to relocate a pole or
zero in the z-plane display, the corresponding real and 
imaginary values in the text fields and the corresponding 
angle and length are automatically updated to reflect the 
new location for the pole or zero.

Note that mainly for convenience (but for technical reasons
as well), the angle and length in the text fields and the
location of the pole or zero in the Z-plane display are 
updated as the user enters each character into the text 
field.  If the user enters text into the text field that 
cannot be converted into a numeric value of type double, 
(such as the pair of characters "-." for example) the 
contents of the text field are automatically converted to a
single "0" character.  A warning message is displayed on 
the command-line screen when this happens.  There is no 
long-term harm when this occurs, but the user may need to 
start over to enter the new value.  Thus, the user should
exercise some care regarding the order in which the 
characters in the text field are modified when entering new
real and imaginary values.

Each time the impulse response and the spectral data are 
plotted, the seventeen feed-forward filter coefficients and
the sixteen feedback coefficients used by the recursive 
filter to produce the output being plotted are displayed on
the command-line screen.

Usage: This program requires access to the following source
code or class files, which were published in earlier 
tutorials:

GraphIntfc01
ForwardRealToComplexFFT01
Graph03

Enter the following command at the command prompt to run 
the program:

java Graph03 Dsp046.

Tested using J2SE 5.0 under WinXP.  J2SE 5.0 or later is
required due to the use of static imports and printf.
**********************************************************/
import static java.lang.Math.*;
import java.awt.*;
import java.awt.event.*;
import javax.swing.*;

class Dsp046 implements GraphIntfc01{
  
  //The value stored in the following variable specifies
  // the number of samples of the impulse response that are
  // captured.  The impulse response serves as the input to
  // an FFT for the purpose of estimating the amplitude and
  // phase response of the recursive filter.  This data
  // length must be a power of 2 for the FFT program to
  // work correctly.  If the user enters a value for the
  // data length that is not a power of two, the value is
  // automatically converted to a power of two by the
  // program.
  int dataLength;
  double[] impulseResponse;
  double[] fourierAmplitudeRespnse;
  double[] fourierPhaseAngle;
  double[] vectorAmplitudeResponse;
  double[] vectorPhaseAngle;
  //This variable contains a reference to a user input GUI
  // containing buttons, radio buttons, and text fields.
  InputGUI inputGUI = null;
  //-----------------------------------------------------//

  Dsp046(){//constructor
    //If the InputGUI object doesn't already exist,
    // create it.  However, if it already exists, retrieve
    // the reference to the object from a static variable
    // belonging to the InputGUI class.  This is
    // necessary because a new object of the Dsp046 class
    // is instantiated each time the user clicks the Graph
    // button on the main (Graph03) GUI.  However, the
    // InputGUI object needs to persist across many
    // clicks of that button because it stores the state of
    // the poles and zeros designed by the user. When the
    // InputGUI object is first created, its pole and
    // zero text fields are initialized with a set of 
    // default pole and zero data values.  Its data length
    // text field is initialized to 1024 samples.
    if(InputGUI.refToObj == null){
      //Instantiate a new InputGUI object.
      inputGUI = new InputGUI();

      //Initialize the length of the array objects that
      // will contain pole and zero data to a value that is
      // maintained in the InputGUI object.
      double[] defaultPoleReal = 
                        new double[inputGUI.numberPoles/2];
      double[] defaultPoleImag = 
                        new double[inputGUI.numberPoles/2];
      double[] defaultZeroReal = 
                        new double[inputGUI.numberZeros/2];
      double[] defaultZeroImag = 
                        new double[inputGUI.numberZeros/2];

      //Create the default data for eight pairs of complex
      // conjugate poles spaced at 20-degree intervals
      // around the unit circle.  These are the locations
      // of the poles in the complex z-plane.  The poles
      // are barely (0.995) inside the unit circle.
      for(int cnt = 0;cnt < inputGUI.numberPoles/2;cnt++){
        defaultPoleReal[cnt] = 
                           0.995*cos((20+20*cnt)*PI/180.0);
        defaultPoleImag[cnt] = 
                           0.995*sin((20+20*cnt)*PI/180.0);
      }//end for loop
  
      //Create the default data for eight pairs of complex
      // conjugate zeros spaced at 20-degree intervals
      // around the unit circle.  These are the locations
      // of the zeros in the complex z-plane.  The zero
      // positions are half way between the pole positions.
      for(int cnt = 0;cnt < inputGUI.numberZeros/2;cnt++){
        defaultZeroReal[cnt] = 
                           0.995*cos((10+20*cnt)*PI/180.0);
        defaultZeroImag[cnt] = 
                           0.995*sin((10+20*cnt)*PI/180.0);
      }//end for loop
    
      //At various points in the program, you may notice
      // that I have performed separate iterations on
      // poles and zeros even though the number of poles
      // is the same as the number of zeros, and I could
      // have combined them.  I did this to make it
      // possible to modify the number of poles or the
      // number of zeros later without the requirement for
      // a major overhaul of the program source code.
    
      //Initialize the real and imaginary text fields in
      // the InputGUI object with the default real and
      // imaginary pole and zero values.
      //Start by setting the pole values.
      for(int cnt = 0;cnt < inputGUI.numberPoles/2;cnt++){
        inputGUI.poleReal[cnt].setText(
                     String.valueOf(defaultPoleReal[cnt]));
        inputGUI.poleImag[cnt].setText(
                     String.valueOf(defaultPoleImag[cnt]));
      }//end for loop

      //Now set the zero values.
      for(int cnt = 0;cnt < inputGUI.numberZeros/2;cnt++){
        inputGUI.zeroReal[cnt].
             setText(String.valueOf(defaultZeroReal[cnt]));
        inputGUI.zeroImag[cnt].setText(
                     String.valueOf(defaultZeroImag[cnt]));
      }//end for loop

      //Get the default data length from the new object.
      // There is no requirement to convert it to a power
      // of two because a power of two is hard-coded into
      // the program as the default value.
      dataLength = Integer.parseInt(
                       inputGUI.dataLengthField.getText());
      
    }else{//An InputGUI object already exists.
      //Retrieve the reference to the existing object that
      // was saved earlier.
      inputGUI = InputGUI.refToObj;
      //Get the current data length from the object.  This
      // value may have been modified by the user and may
      // not be an even power of two.  Convert it to an
      // even power of two and store the converted value
      // back into the text field in the existing object.
      dataLength = Integer.parseInt(
                       inputGUI.dataLengthField.getText());
      dataLength = convertToPowerOfTwo(dataLength);
      inputGUI.dataLengthField.setText("" + dataLength);
    }//end if
    
    //Establish the length of some arrays based on the
    // current data length
    impulseResponse = new double[dataLength];
    fourierAmplitudeRespnse = new double[dataLength];
    fourierPhaseAngle = new double[dataLength];

    //Compute and save the impulse response of the filter.
    // The following code implements a recursive filtering
    // operation based on the poles and zeros previously
    // established.  However, the conversion from poles
    // and zeros to feedForward and feedback coefficients
    // are not routinely involved in the application of a
    // recursive filter to input data. Therefore, there is
    // more code here than would be needed for a routine
    // recursive filtering operation.
    
    //Invoke the captureTextFieldData method on the
    // InputGUI object to cause the current values in the
    // text fields describing the poles and zeros to be
    // converted into double values and stored in arrays.
    inputGUI.captureTextFieldData();
    
    //Create the feedback coefficient array based on the
    // values stored in the text fields of the InputGUI
    // object.  The process is to first multiply the roots
    // corresponding to each of eight pairs of complex
    // conjugate poles.  This produces eight second-order
    // polynomials.  These second-order polynomials are
    // multiplied in pairs to produce four fourth-order
    // polynomials.  These four fourth-order polynomials
    // are multiplied in pairs to produce two eighth-order
    // polynomials.  The two eighth-order polynomials are
    // multiplied to produce one sixteenth-order
    // polynomial.
    //The algebraic sign of the real and imag values were
    // changed to make them match the format of a root
    // located at a+jb.  The format of the root is
    // (x-a-jb)
    //Multiply two pairs of complex conjugate roots to
    // produce two second-order polynomials.
    double[] temp1 = conjToSecondOrder(
      -inputGUI.poleRealData[0],-inputGUI.poleImagData[0]);
    double[] temp2 = conjToSecondOrder(
      -inputGUI.poleRealData[1],-inputGUI.poleImagData[1]);
    //Multiply a pair of second-order polynomials to
    // produce a fourth-order polynomial.
    double[] temp3 = secondToFourthOrder(
                      temp1[1],temp1[2],temp2[1],temp2[2]);

    //Multiply two pairs of complex conjugate roots to
    // produce two second-order polynomials.
    double[] temp4 = conjToSecondOrder(
      -inputGUI.poleRealData[2],-inputGUI.poleImagData[2]);
    double[] temp5 = conjToSecondOrder(
      -inputGUI.poleRealData[3],-inputGUI.poleImagData[3]);
    //Multiply a pair of second-order polynomials to
    // produce a fourth-order polynomial.
    double[] temp6 = secondToFourthOrder(
                      temp4[1],temp4[2],temp5[1],temp5[2]);
    //Multiply a pair of fourth-order polynomials to
    // produce an eighth-order polynomial.
    double[] temp7 = fourthToEighthOrder(
                      temp3[1],temp3[2],temp3[3],temp3[4],
                      temp6[1],temp6[2],temp6[3],temp6[4]);
                      
    //Multiply two pairs of complex conjugate roots to
    // produce two second-order polynomials.
    double[] temp11 = conjToSecondOrder(
      -inputGUI.poleRealData[4],-inputGUI.poleImagData[4]);
    double[] temp12 = conjToSecondOrder(
      -inputGUI.poleRealData[5],-inputGUI.poleImagData[5]);
    //Multiply a pair of second-order polynomials to
    // produce a fourth-order polynomial.
    double[] temp13 = secondToFourthOrder(
                  temp11[1],temp11[2],temp12[1],temp12[2]);

    //Multiply two pairs of complex conjugate roots to
    // produce two second-order polynomials.
    double[] temp14 = conjToSecondOrder(
      -inputGUI.poleRealData[6],-inputGUI.poleImagData[6]);
    double[] temp15 = conjToSecondOrder(
      -inputGUI.poleRealData[7],-inputGUI.poleImagData[7]);
    //Multiply a pair of second-order polynomials to
    // produce a fourth-order polynomial.
    double[] temp16 = secondToFourthOrder(
                  temp14[1],temp14[2],temp15[1],temp15[2]);
    //Multiply a pair of fourth-order polynomials to
    // produce an eighth-order polynomial.
    double[] temp17 = fourthToEighthOrder(
                  temp13[1],temp13[2],temp13[3],temp13[4],
                  temp16[1],temp16[2],temp16[3],temp16[4]);

    //Perform the final polynomial multiplication,
    // multiplying a pair of eighth-order polynomials to
    // produce a sixteenth-order polynomial.  Place the
    // coefficients of the sixteenth-order polynomial in
    // the feedback coefficient array.
    double[] feedbackCoefficientArray = 
                eighthToSixteenthOrder(
                  temp7[1],temp7[2],temp7[3],temp7[4],
                  temp7[5],temp7[6],temp7[7],temp7[8],
                  temp17[1],temp17[2],temp17[3],temp17[4],
                  temp17[5],temp17[6],temp17[7],temp17[8]);

    //Determine the length of the delay line required to
    // perform the feedback arithmetic.
    int feedbackDelayLineLength = 
                           feedbackCoefficientArray.length;
    
    //Create the feedForward coefficient array based on
    // the values stored in the text fields of the
    // InputGUI object.  The process is  the same as
    // described above for the poles.
    
    //Multiply two pairs of complex conjugate roots to
    // produce two second-order polynomials.
    double[] temp21 = conjToSecondOrder(
      -inputGUI.zeroRealData[0],-inputGUI.zeroImagData[0]);
    double[] temp22 = conjToSecondOrder(
      -inputGUI.zeroRealData[1],-inputGUI.zeroImagData[1]);
    //Multiply a pair of second-order polynomials to
    // produce a fourth-order polynomial.
    double[] temp23 = secondToFourthOrder(
                  temp21[1],temp21[2],temp22[1],temp22[2]);

    //Multiply two pairs of complex conjugate roots to
    // produce two second-order polynomials.
    double[] temp24 = conjToSecondOrder(
      -inputGUI.zeroRealData[2],-inputGUI.zeroImagData[2]);
    double[] temp25 = conjToSecondOrder(
      -inputGUI.zeroRealData[3],-inputGUI.zeroImagData[3]);
    //Multiply a pair of second-order polynomials to
    // produce a fourth-order polynomial.
    double[] temp26 = secondToFourthOrder(
                  temp24[1],temp24[2],temp25[1],temp25[2]);
    //Multiply a pair of fourth-order polynomials to
    // produce an eighth-order polynomial.
    double[] temp27 = fourthToEighthOrder(
                  temp23[1],temp23[2],temp23[3],temp23[4],
                  temp26[1],temp26[2],temp26[3],temp26[4]);

    //Multiply two pairs of complex conjugate roots to
    // produce two second-order polynomials.
    double[] temp31 = conjToSecondOrder(
      -inputGUI.zeroRealData[4],-inputGUI.zeroImagData[4]);
    double[] temp32 = conjToSecondOrder(
      -inputGUI.zeroRealData[5],-inputGUI.zeroImagData[5]);
    //Multiply a pair of second-order polynomials to
    // produce a fourth-order polynomial.
    double[] temp33 = secondToFourthOrder(
                  temp31[1],temp31[2],temp32[1],temp32[2]);

    //Multiply two pairs of complex conjugate roots to
    // produce two second-order polynomials.
    double[] temp34 = conjToSecondOrder(
      -inputGUI.zeroRealData[6],-inputGUI.zeroImagData[6]);
    double[] temp35 = conjToSecondOrder(
      -inputGUI.zeroRealData[7],-inputGUI.zeroImagData[7]);
    //Multiply a pair of second-order polynomials to
    // produce a fourth-order polynomial.
    double[] temp36 = secondToFourthOrder(
                  temp34[1],temp34[2],temp35[1],temp35[2]);
    //Multiply a pair of fourth-order polynomials to
    // produce an eighth-order polynomial.
    double[] temp37 = fourthToEighthOrder(
                  temp33[1],temp33[2],temp33[3],temp33[4],
                  temp36[1],temp36[2],temp36[3],temp36[4]);

    //Perform the final polynomial multiplication,
    // multiplying a pair of eighth-order polynomials to
    // produce a sixteenth-order polynomial.  Place the
    // coefficients of the sixteenth-order polynomial in
    // the feedForward coefficient array.
    double[] feedForwardCoefficientArray = 
                eighthToSixteenthOrder(
                  temp27[1],temp27[2],temp27[3],temp27[4],
                  temp27[5],temp27[6],temp27[7],temp27[8],
                  temp37[1],temp37[2],temp37[3],temp37[4],
                  temp37[5],temp37[6],temp37[7],temp37[8]);

    //Determine the length of the delay line required to
    // perform the feedForward arithmetic.
    int feedForwardDelayLineLength = 
                        feedForwardCoefficientArray.length;

    //Display the feedForward and feedback coefficients
    System.out.println(
                  "Feed-Forward (Numerator) Coefficients");
    for(int cnt = 0;
            cnt < feedForwardCoefficientArray.length;
            cnt++){
      System.out.printf ("%2d % 5.3f%n",cnt,
                         feedForwardCoefficientArray[cnt]);
    }//end for loop
    
    System.out.println(
                  "\nFeedback (Denominator) Coefficients");
    for(int cnt = 1;
            cnt < feedbackCoefficientArray.length;
            cnt++){
      System.out.printf ("%2d % 5.3f%n",cnt,
                            feedbackCoefficientArray[cnt]);
    }//end for loop
    System.out.println();

    //Create the data delay lines used for feedForward
    // and feedback arithmetic.
    double[] feedForwardDelayLine = 
                    new double[feedForwardDelayLineLength];
    double[] feedbackDelayLine = 
                       new double[feedbackDelayLineLength];
    
    //Initial input and output data values
    double filterInputSample = 0;//input data
    double filterOutputSample = 0;//output data
    
    //Compute the output values and populate the output
    // array for further analysis such as FFT analysis.
    // This is the code that actually applies the
    // recursive filter to the input data given the
    // feedForward and feedback coefficients.
    for(int dataLenCnt = 0;dataLenCnt < dataLength;
                                             dataLenCnt++){
      //Create the input samples consisting of a single
      // impulse at time zero and sample values of 0
      // thereafter.
      if(dataLenCnt == 0){
        filterInputSample = 100.0;
      }else{
        filterInputSample = 0.0;
      }//end else

      //*************************************************//
      //This is the beginning of one cycle of the actual
      // recursive filtering process.
      
      //Shift the data in the delay lines.  Oldest value
      // has the highest index value.
      for(int cnt = feedForwardDelayLineLength-1; 
                                            cnt > 0;cnt--){
        feedForwardDelayLine[cnt] = 
                               feedForwardDelayLine[cnt-1];
      }//end for loop
  
      for(int cnt = feedbackDelayLineLength-1; 
                                            cnt > 0;cnt--){
        feedbackDelayLine[cnt] = feedbackDelayLine[cnt-1];
      }//end for loop
     
      //Insert the input signal into the delay line at
      // zero index.
      feedForwardDelayLine[0] = filterInputSample;
      
      //Compute sum of products for input signal and
      // feedForward coefficients from 0 to
      // feedForwardDelayLineLength-1.
      double xTemp = 0;
      for(int cnt = 0;cnt < feedForwardDelayLineLength;
                                                    cnt++){
        xTemp += feedForwardCoefficientArray[cnt]*
                                 feedForwardDelayLine[cnt];
      }//end for loop
  
      //Compute sum of products for previous output values
      // and feedback coefficients from 1 to
      // feedbackDelayLineLength-1.
      double yTemp = 0;
      for(int cnt = 1;cnt < feedbackDelayLineLength;cnt++){
        yTemp += feedbackCoefficientArray[cnt]*
                                    feedbackDelayLine[cnt];
      }//end for loop
      
      //Compute new output value as the difference.
      filterOutputSample = xTemp - yTemp;
      
      //Save the output value in the array containing the
      // impulse response.
      impulseResponse[dataLenCnt] = filterOutputSample;
      
      //Insert the output signal into the delay line at
      // zero index.
      feedbackDelayLine[0] = filterOutputSample;
      
      //This is the end of one cycle of the recursive
      // filtering process.
      //*************************************************//
    }//end for loop
    
    //Now compute the Fourier Transform of the impulse
    // response, placing the magnitude result from the FFT
    // program into the fourierAmplitudeRespnse array  and
    // the phase angle result in the fourierPhaseAngle
    // array, each to be plotted later.
    ForwardRealToComplexFFT01.transform(
                                  impulseResponse,
                                  new double[dataLength],
                                  new double[dataLength],
                                  fourierPhaseAngle,
                                  fourierAmplitudeRespnse);
                                    
    /*DO NOT DELETE THIS CODE
    //Note that this normalization code is redundant
    // because of the normalization that takes place in
    // the method named convertToDB later.  However, if
    // the conversion to decibels is disabled, the
    // following code should be enabled.
    //Scale the fourierAmplitudeRespnse to compensate for
    // the differences in data length.
    for(int cnt = 0;cnt < fourierAmplitudeRespnse.length;
                                                    cnt++){
      fourierAmplitudeRespnse[cnt] = 
           fourierAmplitudeRespnse[cnt]*dataLength/16384.0;
    }//end for loop
    */

    //Compute the amplitude response based on the ratio of
    // the products of the pole and zero vectors.  
    vectorAmplitudeResponse = getVectorAmplitudeResponse(
                                    inputGUI.poleRealData,
                                    inputGUI.poleImagData,
                                    inputGUI.zeroRealData,
                                    inputGUI.zeroImagData);

    //Compute the phase angle based on sum and difference
    // of the angles of the pole and zero vectors.
    vectorPhaseAngle = getVectorPhaseAngle(
                                    inputGUI.poleRealData,
                                    inputGUI.poleImagData,
                                    inputGUI.zeroRealData,
                                    inputGUI.zeroImagData);
                                 
    //Convert the fourierAmplitudeRespnse data to decibels.
    // Disable the following statement to disable the
    // conversion to decibels.
    convertToDB(fourierAmplitudeRespnse);
    
    //Convert the vectorAmplitudeResponse to decibels.
    // Disable the following statement to disable the
    // conversion to decibels.
    convertToDB(vectorAmplitudeResponse);
      
  }//end constructor
  //-----------------------------------------------------//
  
  //The purpose of this method is to convert an incoming
  // array containing amplitude response data to decibels.
  void convertToDB(double[] magnitude){
    //Eliminate or modify all values that are incompatible
    // with conversion to log base 10 and the log10 method.
    //  Also limit small values to be no less than 0.0001.
    for(int cnt = 0;cnt < magnitude.length;cnt++){
      if((magnitude[cnt] == Double.NaN) || 
                               (magnitude[cnt] <= 0.0001)){
        magnitude[cnt] = 0.0001;
      }else if(magnitude[cnt] == Double.POSITIVE_INFINITY){
        magnitude[cnt] = 9999999999.0;
      }//end else if
    }//end for loop
    
    //Find the peak value for use in normalization.
    double peak = -9999999999.0;
    for(int cnt = 0;cnt < magnitude.length;cnt++){
      if(peak < abs(magnitude[cnt])){
        peak = abs(magnitude[cnt]);
      }//end if
    }//end for loop

    //Normalize to the peak value to make the values easier
    // to plot with regard to scaling.
    for(int cnt = 0;cnt < magnitude.length;cnt++){
      magnitude[cnt] = magnitude[cnt]/peak;
    }//end for loop
    
    //Now convert normalized magnitude data to log base 10.
    for(int cnt = 0;cnt < magnitude.length;cnt++){
      magnitude[cnt] = log10(magnitude[cnt]);
    }//end for loop
    
  }//end convertToDB
  //-----------------------------------------------------//
  
  //This method makes certain that the incoming value is a
  // non-zero positive power of two that is less than or
  // equal to 16384. If the input is not equal to either a
  // power of two or one less than a power of two, it is
  // truncated to the next lower power of two.  If it is
  // either a power of two or one less than a power of two,
  // the returned value is that power of two.  Negative
  // input values are converted to positive values before
  // making the conversion.
  int convertToPowerOfTwo(int dataLength){
    //Eliminate negative values
    dataLength = abs(dataLength);
    //Make sure the data length is not zero by adding a
    // value of 1.
    dataLength++;
    //Make sure the data length is not greater than 16384.
    if(dataLength > 16384){
      dataLength = 16384;
    }//end if
    
    int cnt = 0;
    int mask = 0x4000;
    //Loop and left shift left until the msb of the data
    // length value matches 0x4000.  Count the number of
    // shifts required to make the match.  No shifts are
    // required for a data length of 16384.
    while((dataLength & mask) == 0){
      cnt++;
      dataLength = dataLength << 1;
    }//end while loop

    //Now shift the mask to the right the same number of
    // places as were required to make the above match.
    // Because the mask consists of a single bit, this
    // guarantees that the resulting value is an even
    // power of two.
    dataLength = mask >> cnt;

    return dataLength;
  }//end convertToPowerOfTwo
  //-----------------------------------------------------//

  //The amplitude response of the recursive filter at a
  // given frequency (a point on the unit circle) can be
  // estimated by dividing the product of the lengths of
  // the vectors connecting that point on the unit circle
  // to all of the zeros by the product of the lengths of
  // the vectors connecting the same point on the unit
  // circle to all of the poles.  The amplitude response
  // at all frequencies between zero and the Nyquist
  // folding frequency can be estimated by performing this
  // calculation at all points in the top half of the unit
  // circle.
  //The bottom half of the unit circle provides the
  // amplitude response for frequencies between the Nyquist
  // folding frequency and the sampling frequency. These
  // values are redundant because they are the same as the
  // values below the folding frequency.
  //Despite the redundancy, this method computes the
  // amplitude response at a set of frequencies between
  // zero and the sampling frequency where the number of
  // frequencies in the set is equal to the data length.
  // This causes the amplitude response to be computed at
  // a set of frequencies that matches the set of
  // frequencies for which the amplitude response is
  // computed using the FFT algorithm, making it easier
  // to plot the two for comparison purposes.
  double[] getVectorAmplitudeResponse(
                                    double[] poleRealData,
                                    double[] poleImagData,
                                    double[] zeroRealData,
                                    double[] zeroImagData){
    double[] amplitudeResponse = new double[dataLength];
    double freqAngle = 0;
    double freqHorizComponent = 0;
    double freqVertComponent = 0;
    
    //Divide the unit circle into dataLength frequencies
    // and compute the amplitude response at each
    // frequency.
    for(int freqCnt = 0;freqCnt < dataLength;freqCnt++){
      //Get the angle from the origin to the point on the
      // unit circle relative to the horizontal axis.
      freqAngle = freqCnt*2*PI/dataLength;

      //Get the horizontal and vertical components of the
      // distance from the origin to the point on the unit
      // circle.
      freqHorizComponent = cos(freqAngle);
      freqVertComponent = sin(freqAngle);
      
      //Compute the product of the lengths from the point
      // on the unit circle to each of the zeros.
      //Get the distance from the point on the unit circle
      // to each zero as the square root of the sum of the
      // squares of the sides of a right triangle formed
      // by the zero and the point on the unit circle with
      // the base of the triangle being parallel to the
      // horizontal axis.
      //Declare some working variables.
      double base;//Base of the right triangle
      double height;//Height of the right triangle
      double hypo;//Hypotenuse of the right triangle
      
      double zeroProduct = 1.0;//Initialize the product.
      //Loop and process all complex conjugate zeros
      for(int cnt = 0;cnt < zeroRealData.length;cnt++){
        //First compute the product for a zero in the
        // upper half of the z-plane
        //Get base of triangle
        base = freqHorizComponent - zeroRealData[cnt];
        //Get height of triangle
        height = freqVertComponent - zeroImagData[cnt];
        //Get hypotenuse of triangle
        hypo = sqrt(base*base + height*height);
        
        //Compute the running product.
        zeroProduct *= hypo;

        //Continue computing the running product using the
        // conjugate zero in the lower half of the z-plane.
        // Note the sign change on the imaginary
        // part.
        base = freqHorizComponent - zeroRealData[cnt];
        height = freqVertComponent + zeroImagData[cnt];
        hypo = sqrt(base*base + height*height);
        zeroProduct *= hypo;
      }//end for loop - all zeros have been processed

      //Now compute the product of the lengths to the
      // poles.
      double poleProduct = 1.0;//Initialize the product.
      for(int cnt = 0;cnt < poleRealData.length;cnt++){
        //Begin with the pole in the upper half of the
        // z-plane.
        base = freqHorizComponent - poleRealData[cnt];
        height = freqVertComponent - poleImagData[cnt];
        hypo = sqrt(base*base + height*height);

        //Compute the running product.
        poleProduct *= hypo;

        //Continue computing the running product using the
        // conjugate pole in the lower half of the z-plane.
        // Note the sign change on the imaginary part.
        base = freqHorizComponent - poleRealData[cnt];
        height = freqVertComponent + poleImagData[cnt];
        hypo = sqrt(base*base + height*height);
        poleProduct *= hypo;//product of lengths
      }//end for loop
      
      //Divide the zeroProduct by the poleProduct.
      //Compute and save the amplitudeResponse for this
      // frequency and then go back to the top of the loop
      // and compute the amplitudeResponse for the next
      // frequency.
      amplitudeResponse[freqCnt] = zeroProduct/poleProduct;
      
    }//end for loop on data length - all frequencies done

    return amplitudeResponse;
  }//end getVectorAmplitudeResponse
  //-----------------------------------------------------//

  //The phase angle of the recursive filter at a
  // particular frequency (represented by a point on the
  // unit circle) can be determined by subtracting the sum
  // of the angles from the point on the unit circle to all
  // of the poles from the sum of the angles from the same
  // point on the unit circle to all of the zeros.
  //The phase angle for an equally-spaced set of
  // frequencies between zero and the sampling frequency is
  // computed in radians and then converted to degrees in
  // the range from -180 degrees to +180 degrees for return
  // to the calling program.
  double[] getVectorPhaseAngle(double[] poleRealData,
                               double[] poleImagData,
                               double[] zeroRealData,
                               double[] zeroImagData){
    double[] phaseResponse = new double[dataLength];
    double freqAngle = 0;
    double freqHorizComponent = 0;
    double freqVertComponent = 0;
    
    //Divide the unit circle into dataLength frequencies
    // and compute the phase angle at each frequency.
    for(int freqCnt = 0;freqCnt < dataLength;freqCnt++){
      //Note that the following reference to an angle is
      // not a reference to the phase angle.  Rather, it
      // is a reference to the angle of a point on the unit
      // circle relative to the horizontal axis and the
      // origin of the z-plane.
      freqAngle = freqCnt * 2 * PI/dataLength;

      //Get the horizontal and vertical components of the
      // distance from the origin to the point on the unit
      // circle.
      freqHorizComponent = cos(freqAngle);
      freqVertComponent = sin(freqAngle);
      
      //Begin by processing all of the complex conjugate
      // zeros.
      //Compute the angle from the point on the unit circle
      // to each of the zeros.  Retain as an angle between
      // zero and 2*PI (360 degrees).
      //Declare some working variables.
      double base;//Base of a right triangle
      double height;//Height of a right triangle
      double zeroAngle;

      double zeroAngleSum = 0;      
      //Loop and process all complex conjugate zeros
      for(int cnt = 0;cnt < zeroRealData.length;cnt++){
        //Compute using the zero in upper the half of the
        // z-plane.
        //Get base of triangle
        base = -(freqHorizComponent - zeroRealData[cnt]);
        //Get height of triangle
        height = -(freqVertComponent - zeroImagData[cnt]);
        
        if(base == 0){//Avoid division by zero.
          zeroAngle = PI/2.0;//90 degees
        }else{//Compute the angle.
          zeroAngle = atan(height/base);
        }//end else

        //Adjust for negative coordinates
        if((base < 0) && (height > 0)){
          zeroAngle = PI + zeroAngle;
        }else if((base < 0) && (height < 0)){
          zeroAngle = PI + zeroAngle;
        }else if((base > 0) && (height < 0)){
          zeroAngle = 2*PI + zeroAngle;
        }//end else
      
        //Compute the running sum of the angles.
        zeroAngleSum += zeroAngle;

        //Continue computing the running sum of angles
        // using the conjugate zero in the lower half of
        // the z-plane.  Note the sign change on the
        // imaginary part.
        base = -(freqHorizComponent - zeroRealData[cnt]);
        height = -(freqVertComponent + zeroImagData[cnt]);

        if(base == 0){
          zeroAngle = 3*PI/2.0;//270 degees
        }else{
          zeroAngle = atan(height/base);
        }//end else
        
        //Adjust for negative coordinates
        if((base < 0) && (height > 0)){
          zeroAngle = PI + zeroAngle;
        }else if((base < 0) && (height < 0)){
          zeroAngle = PI + zeroAngle;
        }else if((base > 0) && (height < 0)){
          zeroAngle = 2*PI + zeroAngle;
        }//end else

        //Add the angle into the running sum of zero
        // angles.
        zeroAngleSum += zeroAngle;

      }//end for loop - all zeros have been processed


      //Now compute the sum of the angles from the point
      // on the unit circle to each of the poles.
      double poleAngle;
      double poleAngleSum = 0;      
      //Loop and process all complex conjugate poles
      for(int cnt = 0;cnt < poleRealData.length;cnt++){
        //Compute using pole in the upper half of the
        // z-plane
        base = -(freqHorizComponent - poleRealData[cnt]);
        height = -(freqVertComponent - poleImagData[cnt]);
        if(base == 0){//Avoid division by zero
          poleAngle = PI/2.0;//90 degees
        }else{
          poleAngle = atan(height/base);
        }//end else

        //Adjust for negative coordinates
        if((base < 0) && (height > 0)){
          poleAngle = PI + poleAngle;
        }else if((base < 0) && (height < 0)){
          poleAngle = PI + poleAngle;
        }else if((base > 0) && (height < 0)){
          poleAngle = 2*PI + poleAngle;
        }//end else

        //Compute the running sum of the angles.
        poleAngleSum += poleAngle;

        //Continue computing the sum of angles using the
        // conjugate pole in the lower half of the Z-plane.
        // Note the sign change on the imaginary part.
        base = -(freqHorizComponent - poleRealData[cnt]);
        height = -(freqVertComponent + poleImagData[cnt]);

        if(base == 0){//Avoid division by 0.
          poleAngle = 3*PI/2.0;//270 degees
        }else{
          poleAngle = atan(height/base);
        }//end else
        
        //Adjust for negative coordinates
        if((base < 0) && (height > 0)){
          poleAngle = PI + poleAngle;
        }else if((base < 0) && (height < 0)){
          poleAngle = PI + poleAngle;
        }else if((base > 0) && (height < 0)){
          poleAngle = 2*PI + poleAngle;
        }//end else

        poleAngleSum += poleAngle;
      }//end for loop - all poles have been processed

      //Subtract the sum of the pole angles from the sum of
      // the zero angles.  Convert the angle from radians
      // to degrees in the process.
      //Note that the minus sign in the following
      // expression is required to cause the sign of the
      // angle computed using this approach to match the
      // sign of the angle computed by the FFT algorithm.
      // This indicates that either this computation or the
      // FFT computation is producing a phase angle having
      // the wrong sign.
      double netAngle = 
                     -(zeroAngleSum - poleAngleSum)*180/PI;
      
      //Normalize the angle to the range from -180 degrees 
      // to +180 degrees to make it easier to plot.
      if(netAngle > 180){
        while(netAngle > 180){
          netAngle -= 360;
        }//end while
      }else if(netAngle < -180){
        while(netAngle < -180){
          netAngle += 360;
        }//end while
      }//end else if

      //Save the phase angle for this frequency and then go
      // back to the top of the loop and compute the phase
      // angle for the next frequency.
      phaseResponse[freqCnt] = netAngle;

    }//end for loop on data length - all frequencies done

    return phaseResponse;
  }//end getVectorPhaseAngle  
  //-----------------------------------------------------//

  //Receives the complex conjugate roots of a second-order
  // polynomial in the form (a+jb)(a-jb).  Multiplies the
  // roots and returns the coefficients of the second-order
  // polynomial as x*x + 2*a*x + (a*a + b*b) in a three
  // element array of type double.
  double[] conjToSecondOrder(double a,double b){
    double[] result = new double[]{1,2*a,(a*a + b*b)};
    return result;
  }//end conjToSecondOrder
  //-----------------------------------------------------//
  
  //Receives the coefficients of a pair of second-order
  // polynomials in the form:
  // x*x + a*x + b
  // x*x + c*x + d
  //Multiplies the polynomials and returns the coefficients
  // of a fourth-order polynomial in a five-element array
  // of type double.
  double[] secondToFourthOrder(double a,double b,
                               double c,double d){
    double[] result = new double[]{1,
                                   a + c,
                                   b + c*a + d,
                                       c*b + d*a,
                                             d*b};
    return result;
  }//end secondToFourthOrder
  //-----------------------------------------------------//
  
  //Receives the coeficients of a pair of fourth order
  // polynomials in the form:
  // x*x*x*x + a*x*x*x + b*x*x + c*x + d
  // x*x*x*x + e*x*x*x + f*x*x + g*x + h
  //Multiplies the polynomials and returns the coefficients
  // of an eighth-order polynomial in a nine-element
  // array of type double.
  double[] fourthToEighthOrder(double a,double b,
                               double c,double d,
                               double e,double f,
                               double g,double h){
    double[] result = new double[]{
                               1,
                               a + e,
                               b + e*a + f,
                               c + e*b + f*a + g,
                               d + e*c + f*b + g*a + h,
                                   e*d + f*c + g*b + h*a,
                                         f*d + g*c + h*b,
                                               g*d + h*c,
                                                     h*d};
    return result;
  }//end fourthToEighthOrder
  //-----------------------------------------------------//
  
  //Receives the coefficients of a pair of eighth order
  // polynomials in the following form where xn indicates
  // x to the nth power:
  // x8 + ax7 + bx6 + cx5 + dx4 + ex3 + fx2 + gx + h
  // x8 + ix7 + jx6 + kx5 + lx4 + mx3 + nx2 + ox + p
  //Multiplies the polynomials and returns the coefficients
  // of a sixteenth-order polynomial in a 17-element
  // array of type double
  double[] eighthToSixteenthOrder(double a,double b,
                                  double c,double d,
                                  double e,double f,
                                  double g,double h,
                                  double i,double j,
                                  double k,double l,
                                  double m,double n,
                                  double o,double p){
    double[] result = new double[]{
                       1,
                       a+i,
                       b+i*a+j,
                       c+i*b+j*a+k,
                       d+i*c+j*b+k*a+l,
                       e+i*d+j*c+k*b+l*a+m,
                       f+i*e+j*d+k*c+l*b+m*a+n,
                       g+i*f+j*e+k*d+l*c+m*b+n*a+o,
                       h+i*g+j*f+k*e+l*d+m*c+n*b+o*a+p,
                         i*h+j*g+k*f+l*e+m*d+n*c+o*b+p*a,
                             j*h+k*g+l*f+m*e+n*d+o*c+p*b,
                                 k*h+l*g+m*f+n*e+o*d+p*c,
                                     l*h+m*g+n*f+o*e+p*d,
                                         m*h+n*g+o*f+p*e,
                                             n*h+o*g+p*f,
                                                 o*h+p*g,
                                                     p*h};
    return result;
  }//end eighthToSixteenthOrder                       
  //-----------------------------------------------------//
  
  //The following six methods are declared in the interface
  // named GraphIntfc01, and are required by the plotting
  // program named Graph03.
  //-----------------------------------------------------//

  //This method specifies the number of functions that will
  // be plotted by the program named Graph03.
  public int getNmbr(){
    //Return number of functions to
    // process.  Must not exceed 5.
    return 5;
  }//end getNmbr
  //-----------------------------------------------------//

  //This method returns the values that will be plotted in
  // the first graph by the program named Graph03.
  public double f1(double x){
    //Return the impulse response of the filter.
    if(((int)x >= 0) && ((int)x < impulseResponse.length)){
      return impulseResponse[(int)x];
    }else{
      return 0;
    }//end else
  }//end f1
  //-----------------------------------------------------//

  //This method returns the values that will be plotted in
  // the second graph by the program named Graph03.
  public double f2(double x){
    //Return the amplitude response of the recursive filter
    // obtained by performing a Fourier Transform on the
    // impulse response and converting the result to 
    // decibels.  Recall that adding a constant to a
    // decibel plot is equivalent to multiplying the 
    // original data by the constant.
    if(((int)x >= 0) && 
                ((int)x < fourierAmplitudeRespnse.length)){
      return 100 + 
                 (100.0 * fourierAmplitudeRespnse[(int)x]);
    }else{
      return 0;
    }//end else
  }//end f2
  //-----------------------------------------------------//

  //This method returns the values that will be plotted in
  // the third graph by the program named Graph03.
  public double f3(double x){
    //Return the amplitude response of the recursive filter
    // obtained by dividing the product of the zero vector
    // lengths by the product of the pole vector lengths
    // and converting the result to decibels.  Recall that
    // adding a constant to a decibel plot is equivalent to
    // multiplying the original data by the constant.
    if(((int)x >= 0) 
             && ((int)x < vectorAmplitudeResponse.length)){
      return 100 + 
                 (100.0 * vectorAmplitudeResponse[(int)x]);
    }else{
      return 0;
    }//end else
  }//end f3
  //-----------------------------------------------------//

  //This method returns the values that will be plotted in
  // the fourth graph by the program named Graph03.
  public double f4(double x){
    //Return the phase response of the recursive filter
    // obtained by performing a Fourier Transform on the
    // impulse response.
    if(((int)x >= 0) && 
                      ((int)x < fourierPhaseAngle.length)){
      return fourierPhaseAngle[(int)x];
    }else{
      return 0;
    }//end else
  }//end f4
  //-----------------------------------------------------//

  //This method returns the values that will be plotted in
  // the fifth graph by the program named Graph03.
  public double f5(double x){
    //Return the phase response of the recursive filter
    // obtained by subtracting the sum of the pole vector
    // angles from the sum of the zero vector angles.
    if(((int)x >= 0) && 
                       ((int)x < vectorPhaseAngle.length)){
      return vectorPhaseAngle[(int)x];
    }else{
      return 0;
    }//end else
  }//end f5

}//end class Dsp046
//=======================================================//



//An object of this class stores and displays the real and
// imaginary parts of sixteen complex poles and sixteen
// complex zeros.  The sixteen poles and sixteen zeros
// form eight conjugate pairs.  Thus, there are eight
// complex conjugate pairs of poles and eight complex
// conjugate pairs of zeros.
//The object also computes and displays the angle in
// degrees for each pole and each zero relative to the
// origin of the z-plane.  It also computes and displays
// the length of an imaginary vector connecting each
// pole and zero to the origin.
//The real and imaginary part for each pole or zero is
// displayed in a TextField object.  The user can modify
// the values by entering new values into the text fields.
// The user can also modify the real and imaginary values
// by selecting a radio button associated with a specific
// pole or zero and then clicking a new location for that
// pole or zero in an auxiliary display that shows the
// complex z-plane and the unit circle in that plane.  When
// the user clicks in the z-plane, the corresponding values
// in the text fields for the selected pole or zero are
// automatically updated.  When the user changes a real
// or imaginary value in a text field, the radio button 
// for that pole or zero is automatically selected, and 
// the image of that pole or zero in the z-plane is 
// automatically changed to show the new position of the
// pole or zero.
//Regardless of which method causes the contents of a text
// field to be modified, a TextListener that is registered
// on the text field causes the displayed angle and length
// to be updated to match the new real and imaginary
// values.
class InputGUI{
  //A reference to an object of this class is stored in the
  // following static variable.  This makes it possible for
  // the original object that created this object to cease
  // to exist without this object becoming eligible for
  // garbage collection.  When that original object is
  // replaced by a new object, the new object can assume
  // ownership of this object by getting its reference from
  // the static variable. Thus, ownership of this object
  // can be passed along from one object to the next.
  static InputGUI refToObj = null;
  
  //The following ButtonGroup object is used to group
  // radio buttons to cause them to behave in a mutually
  // exclusive way.  The zero buttons and the pole buttons
  // are all placed in the same group so that only one zero
  // or one pole can be selected at any point in time.
  ButtonGroup buttonGroup = new ButtonGroup();
  
  //A reference to an auxiliary display showing the
  // z-plane is stored in the following instance variable.
  ZPlane refToZPlane;
  
  //This is the default number of poles and zeros
  // including the conjugates.  These values cannot be
  // changed by the user.  However, the effective number of
  // poles or zeros can be reduced by moving poles and/or
  // zeros to the origin in the z-plane, rendering them
  // ineffective in the recursive filtering process.
  // Moving poles and zeros to the origin causes feedback
  // and feed-forward zeros to go to zero.
  int numberPoles = 16;
  int numberZeros = 16;
  
  //The following variables refer to a pair of buttons used
  // to make it possible for the user to place all the
  // poles and zeros at the origin. In effect, these are
  // reset buttons relative to the pole and zero locations.
  JButton clearPolesButton = 
                       new JButton("Move Poles to Origin");
  JButton clearZerosButton = 
                       new JButton("Move Zeros to Origin");
  
  //The following text field stores the default data length
  // at startup.  This value can be changed by the user to
  // investigate the impact of changes to the data length
  // for a given set of poles and zeros.
  TextField dataLengthField = new TextField("1024");
  
  //The following array objects get populated with numeric
  // values from the text fields by the method named
  // captureTextFieldData.  That method should be called
  // to populate them with the most current text field
  // data when the most current data is needed.
  double[] poleRealData = new double[numberPoles/2];
  double[] poleImagData = new double[numberPoles/2];
  double[] zeroRealData = new double[numberZeros/2];
  double[] zeroImagData = new double[numberZeros/2];

  //The following arrays are populated with references to
  // radio buttons, each of which is associated with a
  // specific pair of complex conjugate poles or zeros.
  JRadioButton[] poleRadioButtons = 
                           new JRadioButton[numberPoles/2];
  JRadioButton[] zeroRadioButtons = 
                           new JRadioButton[numberZeros/2];

  //The following arrays are populated with references to
  // text fields, each of which is associated with a
  // specific pair of complex conjugate poles or zeros. 
  // The text fields contain the real values, imaginary
  // values, and the values of the angle and the length
  // specified by the real and imaginary values.
  //The size of the following arrays is only half the
  // number of poles and zeros because the conjugate is
  // generated on the fly when it is needed.
  //I wanted to use JTextField objects, but JTextField
  // doesn't have an addTextListener method.  I needed to
  // register a TextListener object on each real and
  // imaginary text field to compute the angle and length
  // each time the contents of a text field changes, so I
  // used the AWT TextField class instead.
  TextField[] poleReal = new TextField[numberPoles/2];
  TextField[] poleImag = new TextField[numberZeros/2];  
  TextField[] poleAngle = new TextField[numberZeros/2];
  TextField[] poleLength = new TextField[numberZeros/2];
  TextField[] zeroReal = new TextField[numberZeros/2];
  TextField[] zeroImag = new TextField[numberZeros/2];
  TextField[] zeroAngle = new TextField[numberZeros/2];
  TextField[] zeroLength = new TextField[numberZeros/2];
  //-----------------------------------------------------//
  
  InputGUI(){//constructor
  
    //Instantiate a new JFrame object and condition its
    // close button.
    JFrame guiFrame = 
                  new JFrame("Copyright 2006 R.G.Baldwin");
    guiFrame.setDefaultCloseOperation(
                                     JFrame.EXIT_ON_CLOSE);
    
    //The following JPanel contains a JLabel, a TextField,
    // and two JButton objects.  The label simply provides
    // instructions to the user regarding the entry of a
    // new data length.  The text field is used for entry
    // of a new data length value by the user at runtime.
    // The buttons are used to cause the poles and zeros
    // to be moved to the origin in two groups.  Moving
    // both the poles and the zeros to the origin
    // effectively converts the recursive filter to an
    // all-pass filter.
    //This panel is placed in the NORTH location of the
    // JFrame resulting in the name northControlPanel
    JPanel northControlPanel = new JPanel();
    northControlPanel.setLayout(new GridLayout(0,2));
    northControlPanel.
              add(new JLabel("Data Length as Power of 2"));
    northControlPanel.add(dataLengthField);
    northControlPanel.add(clearPolesButton);
    northControlPanel.add(clearZerosButton);
    guiFrame.add(northControlPanel,BorderLayout.NORTH);
    
    //Register an action listener on the clearPolesButton
    // to set the contents of the text fields that
    // represent the locations of the poles to 0.  This
    // also causes the poles to move to the origin in the
    // display of the z-plane.
    clearPolesButton.addActionListener(
      new ActionListener(){
        public void actionPerformed(ActionEvent e){
          for(int cnt = 0;cnt < numberPoles/2;cnt++){
            poleReal[cnt].setText("0");
            poleImag[cnt].setText("0");
          }//end for loop
        }//end actionPerformed
      }//end new ActionListener
    );//end addActionListener
      
    //Register action listener on the clearZerosButton to
    // set the contents of the text fields that
    // represent the locations of the zeros to 0  This
    // also causes the zeros to move to the origin in the
    // display of the z-plane.
    clearZerosButton.addActionListener(
      new ActionListener(){
        public void actionPerformed(ActionEvent e){
          for(int cnt = 0;cnt < numberZeros/2;cnt++){
            zeroReal[cnt].setText("0");
            zeroImag[cnt].setText("0");
          }//end for loop
        }//end actionPerformed
      }//end new ActionListener
    );//end addActionListener
      
    
    //The following JPanel object contains two other JPanel
    // objects, one for zeros and one for poles.  They 
    // are the same size with one located above the other.
    // The panel containing zero data is green.  The panel
    // containing pole data is yellow.  This panel is
    // placed in the CENTER of the JFrame object.  Hence
    // the name centerControlPanel.
    JPanel centerControlPanel = new JPanel();
    centerControlPanel.setLayout(new GridLayout(2,1));
    
    //The following JPanel is populated with text fields
    // and radio buttons that represent the zeros.
    JPanel zeroPanel = new JPanel();
    zeroPanel.setBackground(Color.GREEN);
    
    //The following JPanel is populated with text fields
    // and radio buttons that represent the poles.
    JPanel polePanel = new JPanel();
    polePanel.setBackground(Color.YELLOW);
    
    //Add the panels containing textfields and readio
    // buttons to the larger centerControlPanel.
    centerControlPanel.add(zeroPanel);
    centerControlPanel.add(polePanel);
    
    //Add the centerControlPanel to the CENTER of the
    // JFrame object.
    guiFrame.getContentPane().add(
                   centerControlPanel,BorderLayout.CENTER);
    
    //Instantiate a text listener that will be registered
    // on each of the text fields containing real and
    // imaginary values, each pair of which specifies the
    // location of a pole or a zero.
    MyTextListener textListener = new MyTextListener();
    
    //A great deal is accomplished in each of the following
    // two for loops.
    //Begin by populating the arrays described earlier with
    // radio buttons and text fields.
    //Then place the radio buttons associated with the
    // poles and zeros in the same group to make them
    // behave in a mutually exclusive manner.
    //Next, place the components on the polePanel and the
    // zero panel.
    //Then disable the text fields containing the angle
    // and the length to prevent the user from entering
    // data into them.  Note that this does not prevent
    // the program from writing text into the text fields
    // containing the angle and the length.  The text
    // fields are disabled only insofar as manual input by
    // the user is concerned.
    //After that, set the name property for each of the
    // real and imaginary text fields.  These name property
    // values will be used later by a common TextListener
    // object to determine which text field fired a
    // TextEvent.
    //Finally, register a common TextListener object on the
    // real and imaginary text fields to cause the angle 
    // and the length to be computed and displayed when the
    // text value changes for any reason.
    
    //Deal with the poles.
    polePanel.setLayout(new GridLayout(0,5));
    //Place a row of column headers
    polePanel.add(new JLabel("Poles"));
    polePanel.add(new JLabel("Real"));
    polePanel.add(new JLabel("Imag"));
    polePanel.add(new JLabel("Angle (deg)"));
    polePanel.add(new JLabel("Length"));
    //Take the actions described above with respect to the
    // poles.
    for(int cnt = 0;cnt < numberPoles/2;cnt++){
      poleRadioButtons[cnt] = new JRadioButton("" + cnt);
      poleReal[cnt] = new TextField("0");
      poleImag[cnt] = new TextField("0");
      poleAngle[cnt] = new TextField("0");
      poleLength[cnt] = new TextField("0");
      buttonGroup.add(poleRadioButtons[cnt]);
      polePanel.add(poleRadioButtons[cnt]);
      polePanel.add(poleReal[cnt]);
      polePanel.add(poleImag[cnt]);
      polePanel.add(poleAngle[cnt]);
      poleAngle[cnt].setEnabled(false);
      polePanel.add(poleLength[cnt]);
      poleLength[cnt].setEnabled(false);      
      poleReal[cnt].setName("poleReal" + cnt);
      poleImag[cnt].setName("poleImag" + cnt);
      poleReal[cnt].addTextListener(textListener);
      poleImag[cnt].addTextListener(textListener);
    }//end for loop

    //Deal with the zeros.
    zeroPanel.setLayout(new GridLayout(0,5));
    //Place a row of column headers
    zeroPanel.add(new JLabel("Zeros"));
    zeroPanel.add(new JLabel("Real"));
    zeroPanel.add(new JLabel("Imag"));
    zeroPanel.add(new JLabel("Angle (deg)"));
    zeroPanel.add(new JLabel("Length"));
    //Now take the actions described above with respect to
    // the zeros.
    for(int cnt = 0;cnt < numberZeros/2;cnt++){
      zeroRadioButtons[cnt] = new JRadioButton("" + cnt);
      zeroReal[cnt] = new TextField("0");
      zeroImag[cnt] = new TextField("0");
      zeroAngle[cnt] = new TextField("0");
      zeroLength[cnt] = new TextField("0");
      buttonGroup.add(zeroRadioButtons[cnt]);
      zeroPanel.add(zeroRadioButtons[cnt]);
      zeroPanel.add(zeroReal[cnt]);
      zeroPanel.add(zeroImag[cnt]);
      zeroPanel.add(zeroAngle[cnt]);
      zeroAngle[cnt].setEnabled(false);
      zeroPanel.add(zeroLength[cnt]);
      zeroLength[cnt].setEnabled(false);      
      zeroReal[cnt].setName("zeroReal" + cnt);
      zeroImag[cnt].setName("zeroImag" + cnt);
      zeroReal[cnt].addTextListener(textListener);
      zeroImag[cnt].addTextListener(textListener);
    }//end for loop

    //Now create an auxiliary display of the z-plane
    // showing a unit circle.  The user locates poles and
    // zeros on it by first selecting the radio button that
    // specifies a particular pole or zero, and then
    // clicking in the z-plane with the mouse.  (Note that
    // locating a pole outside the unit circle should
    // result in an unstable recursive filter with an
    // output that continues to grow with time.)
    refToZPlane = new ZPlane();
    
    //Register an anonymous MouseListerer object on the
    // z-plane.
    refToZPlane.addMouseListener(
      new MouseAdapter(){
        public void mousePressed(MouseEvent e){
          //Get and save the coordinates of the mouse click
          // relative to an origin that has been translated
          // from the upper-left corner to a point near the
          // center of the frame.
          //Change the sign on the vertical coordinate to
          // cause the result to match our expectation of
          // positive vertical values going up the screen
          // instead of going down the screen.
          int realCoor = e.getX() - refToZPlane.
                                      translateOffsetHoriz;
          int imagCoor = -(e.getY() - refToZPlane.
                                      translateOffsetVert);
          
          //The new coordinate values are deposited in the
          // real and imaginary text fields associated with
          // the selected radio button.
          //Examine the radio buttons to identify the pair
          // of real and imaginary text fields into which
          // the new coordinate values should be deposited.
          //Note that one radio button is always selected,
          // so don't click in the z-plane unless you
          // really do want to modify the coordinate values
          // in the text fields associated with the 
          // selected radio button.
          //Note that the integer coordinate values are
          // converted to fractional coordinate values by
          // dividing the integer coordinate values by the
          // radius (in pixels) of the unit circle as
          // displayed on the z-plane.
          
          //Examine the pole buttons first.
          boolean selectedFlag = false;
          for(int cnt = 0;cnt < numberPoles/2;cnt++){
            if(poleRadioButtons[cnt].isSelected()){
              poleReal[cnt].setText("" + (realCoor/
                  (double)(refToZPlane.unitCircleRadius)));
              poleImag[cnt].setText("" + abs(imagCoor/
                  (double)(refToZPlane.unitCircleRadius)));
              //Set the selectedFlag to prevent the zero
              // radio buttons from being examined.
              selectedFlag = true;
              //No other button can be selected.  They are
              // mutually exclusive.
              break;
            }//end if
          }//end for loop
          
          if(!selectedFlag){//Skip if selectedFlag is true.
            //Examine the zero buttons
            for(int cnt = 0;cnt < numberZeros/2;cnt++){
              if(zeroRadioButtons[cnt].isSelected()){
                zeroReal[cnt].setText("" + (realCoor/
                  (double)(refToZPlane.unitCircleRadius)));
                zeroImag[cnt].setText("" + abs(imagCoor/
                  (double)(refToZPlane.unitCircleRadius)));
                break;//No other button can be selected
              }//end if
            }//end for loop
          }//end if on selectedFlag
          
          //Cause the display of the z-plane to be
          // repainted showing the new location for the
          // pole or zero.
          refToZPlane.repaint();
        }//end mousePressed
      }//end new class
    );//end addMouseListener
    
    //Set the size and location of the InputGUI (JFrame)
    // object on the screen.  Position it in the upper
    // right corner of a 1024x768 screen.
    guiFrame.setBounds(1024-472,0,472,400);

    //Cause two displays to become visible.  Prevent the
    // user from resizing them.
    guiFrame.setResizable(false);
    guiFrame.setVisible(true);
    refToZPlane.setResizable(false);
    refToZPlane.setVisible(true);

    //Save the reference to this GUI object so that it can
    // be recovered later after a new instance of the
    // Dsp046 class is instantiated.
    InputGUI.refToObj = this;
  }//end constructor
  //-----------------------------------------------------//
  
  
  //This is a utility method used to capture the latest
  // text field data, convert it into type double, and
  // store the numeric values into arrays.
  //The try-catch handlers are designed to deal with the
  // possibility that a text field contains a text value
  // that cannot be converted to a double value when the
  // method is invoked.  In that case, the value is
  // replaced by 0 and an error message is displayed on
  // the command-line screen. This is likely to happen,
  // for example, if the user deletes the contents of a
  // text field in preparation for entering a new value.
  // In that case, the TextListener will invoke this
  // method in an attempt to compute and display new
  // values for the angle and the length.
  //One way to enter a new value in the text field is to
  // highlight the old value before starting to type the
  // new value.  Although this isn't ideal, it is the best
  // that I could come up with in order to cause the angle
  // and the length to be automatically computed and
  // displayed each time a new value is entered into the
  // text field.
  void captureTextFieldData(){
    //Encapsulate the pole data in an array object.
    for(int cnt = 0;cnt < numberPoles/2;cnt++){
      try{
        poleRealData[cnt] = 
               Double.parseDouble(poleReal[cnt].getText());
      }catch(NumberFormatException e){
        //The text in the text field could not be converted
        // to type double.
        poleReal[cnt].setText("0");
        System.out.println("Warning: Illegal entry for " +
               "poleReal[" + cnt + "], " + e.getMessage());
      }//end catch
      
      try{
        poleImagData[cnt] = 
               Double.parseDouble(poleImag[cnt].getText());
      }catch(NumberFormatException e){
        poleImag[cnt].setText("0");
        System.out.println("Warning: Illegal entry for " +
               "poleImag[" + cnt + "], " + e.getMessage());
      }//end catch
    }//end for loop

    //Encapsulate the zero data in an array object.
    for(int cnt = 0;cnt < numberZeros/2;cnt++){
      try{
        zeroRealData[cnt] = 
               Double.parseDouble(zeroReal[cnt].getText());
      }catch(NumberFormatException e){
        zeroReal[cnt].setText("0");
        System.out.println("Warning: Illegal entry for " +
               "zeroReal[" + cnt + "], " + e.getMessage());
      }//end catch
      
      try{
        zeroImagData[cnt] = 
               Double.parseDouble(zeroImag[cnt].getText());
      }catch(NumberFormatException e){
        zeroImag[cnt].setText("0");
        System.out.println("Warning: Illegal entry for " +
               "zeroImag[" + cnt + "], " + e.getMessage());
      }//end catch
    }//end for loop

  }//end captureTextFieldData method
  //-----------------------------------------------------//
  
//=======================================================//
//This is an inner text listener class.  A registered
// object of the class is notified whenever the text value
// for any of the real or imaginary values in the pole and
// zero text fields changes for any reason.  When the
// event handler is notified, it computes and displays the
// angle specified by the ratio of the imaginary part to
// the real part.  All angles are expressed in degrees
// between 0 and 359.9 inclusive.  
//Also, when notified, the event handler computes the
// length of an imaginary vector connecting the pole or
// zero to the origin as the square root of the sum of the
// squares of the real and imaginary parts.
//Finally, the event handler also causes the z-plane to be
// repainted to display the new location for the pole or
// zero represented by the text field that fired the event.
class MyTextListener implements TextListener{
  
  public void textValueChanged(TextEvent e){
    //Invoke the captureTextFieldData method to cause the
    // latest values in the text fields to be converted to
    // numeric double values and stored in arrays.
    captureTextFieldData();

    //Identify the text field that fired the event and
    // respond appropriately.  Cause the radio button
    // associated with the modified text field to become
    // selected.
    boolean firingObjFound = false;
    String name = ((Component)e.getSource()).getName();
    for(int cnt = 0;cnt < numberPoles/2;cnt++){
      if((name.equals("poleReal" + cnt)) || 
                          (name.equals("poleImag" + cnt))){
        //Compute and set the angle to the pole.
        poleAngle[cnt].setText(getAngle(
                     poleRealData[cnt],poleImagData[cnt]));
        //Compute and set the length of an imaginary vector
        // connecting the pole to the origin.
        poleLength[cnt].setText("" + sqrt(
                     poleRealData[cnt]*poleRealData[cnt] +
                     poleImagData[cnt]*poleImagData[cnt]));
        //Select the radio button.
        poleRadioButtons[cnt].setSelected(true);
        firingObjFound = true;//Avoid testing zeros
        break;
      }//end if
    }//end for loop

    if(!firingObjFound){
      for(int cnt = 0;cnt < numberZeros/2;cnt++){
        if((name.equals("zeroReal" + cnt)) || 
                          (name.equals("zeroImag" + cnt))){
          //Compute and set the angle to the zero.
          zeroAngle[cnt].setText(getAngle(
                     zeroRealData[cnt],zeroImagData[cnt]));
          //Compute and set the length of an imaginary
          // vector connecting the zero to the origin.
          zeroLength[cnt].setText("" + sqrt(
                     zeroRealData[cnt]*zeroRealData[cnt] +
                     zeroImagData[cnt]*zeroImagData[cnt]));
          //Select the radio button.
          zeroRadioButtons[cnt].setSelected(true);
          break;
        }//end if
      }//end for loop
    }//end if on firingObjFound
    
    //Repaint the z-plane to show the new pole or zero
    // location.
    refToZPlane.repaint();
    
  }//end textValueChanged
  //-----------------------------------------------------//
 
  //This method returns the angle in degrees indicated by
  // the incoming real and imaginary values in the range
  // from 0 to 359.9 degrees.
  String getAngle(double realVal,double imagVal){
    String result = "";
    //Avoid division by 0
    if((realVal == 0.0) && (imagVal >= 0.0)){
      result = "" + 90;
    }else if((realVal == 0.0) && (imagVal < 0.0)){
      result = "" + 270;
    }else{
      //Compute the angle in radians.
      double angle = atan(imagVal/realVal);

      //Adjust for negative coordinates
      if((realVal < 0) && (imagVal == 0.0)){
        angle = PI;
      }else if((realVal < 0) && (imagVal > 0)){
        angle = PI + angle;
      }else if((realVal < 0) && (imagVal < 0)){
        angle = PI + angle;
      }else if((realVal > 0) && (imagVal < 0)){
        angle = 2*PI + angle;
      }//end else
    
      //Convert from radians to degrees
      angle = angle*180/PI;
   
      //Convert the angle from double to String.
      String temp1 = "" + angle;
      if(temp1.length() >= 5){
        result = temp1.substring(0,5);
      }else{
        result = temp1;
      }//end else
    }//end else
    return result;
  }//end getAngle
  //-----------------------------------------------------//
}//end inner class MyTextListener
//=======================================================//

//This is an inner class.  An object of this class is
// an auxiliary display that represents the z-plane.
class ZPlane extends Frame{
  Insets insets;
  int totalWidth;
  int totalHeight;
  //Set the size of the display area in pixels.
  int workingWidth = 464;
  int workingHeight = 464;
  int unitCircleRadius = 200;//Radius in pixels.
  int translateOffsetHoriz;
  int translateOffsetVert;
  
  ZPlane(){//constructor
    //Get the size of the borders and the banner.  Set the
    // overall size to accommodate them and still provide
    // a display area whose size is specified by
    // workingWidth and workingHeight.
    //Make the frame visible long enough to get the values
    // of the insets.
    setVisible(true);
    insets = getInsets();
    setVisible(false);
    totalWidth = workingWidth + insets.left + insets.right;
    totalHeight = 
                workingHeight + insets.top + insets.bottom;
    setTitle("Copyright 2006, R.G.Baldwin");
    
    //Set the size of the new Frame object so that it will
    // have a working area that is specified by
    // workingWidth and workingHeight. Elsewhere in the
    // program, the resizable property of the Frame is set
    // to false so that the user cannot modify the size.

    //Locate the Frame object in the upper-center of the
    // screen
    setBounds(408,0,totalWidth,totalHeight);
    
    //Move the origin to the center of the working area.
    // Note, however, that the direction of positive-y is
    // down the screen.  This will be compensated for
    // elsewhere in the program.
    translateOffsetHoriz = workingWidth/2 + insets.left;
    translateOffsetVert = workingHeight/2 + insets.top;
    
    //Register a window listener that can be used to
    // terminate the program by clicking the X-button in
    // the upper right corner of the frame.
    addWindowListener(
      new WindowAdapter(){
        public void windowClosing(WindowEvent e){
          System.exit(0);//terminate the program
        }//end windowClosing
      }//end class def
    );//end addWindowListener
  }//end constructor
  //-----------------------------------------------------//
  
  //This overridden paint method is used to repaint the
  // ZPlane object when the program requests a repaint on
  // the object.
  public void paint(Graphics g){
    //Translate the origin to the center of the working
    // area in the frame.
    g.translate(translateOffsetHoriz,translateOffsetVert);
    //Draw a round oval to represent the unit circle in the
    // z-plane.
    g.drawOval(-unitCircleRadius,-unitCircleRadius,
               2*unitCircleRadius,2*unitCircleRadius);
    //Draw horizontal and vertical axes at the new origin.
    g.drawLine(-workingWidth/2,0,workingWidth/2,0);
    g.drawLine(0,-workingHeight/2,0,workingHeight/2);
    
    //Invoke the captureTextFieldData method to cause the
    // latest data in the text fields to be converted to
    // double numeric values and stored in arrays.
    captureTextFieldData();
    
    //Draw the poles in red using the data retrieved from
    // the text fields.  Note that the unitCircleRadius in
    // pixels is used to convert the locations of the
    // poles from double values to screen pixels.
    g.setColor(Color.RED);
    
    for(int cnt = 0;cnt < poleRealData.length;cnt++){
      //Draw the conjugate pair of poles as small red
      // squares centered on the poles.
      int realInt = 
                 (int)(poleRealData[cnt]*unitCircleRadius);
      int imagInt = 
                 (int)(poleImagData[cnt]*unitCircleRadius);
      //Draw the pair of conjugate poles.
      g.drawRect(realInt-2,imagInt-2,4,4);
      g.drawRect(realInt-2,-imagInt-2,4,4);
    }//end for loop
    
    //Draw the zeros in black using the data retrieved from
    // the text fields.  Note that the unitCircleRadius in
    // pixels is used to convert the locations of the
    // zeros from double values to screen pixels.

    g.setColor(Color.BLACK);//Restore color to black
    
    for(int cnt = 0;cnt < zeroRealData.length;cnt++){
      //Draw the conjugate pair of zeros as small black
      // circles centered on the zeros.
      int realInt = 
                 (int)(zeroRealData[cnt]*unitCircleRadius);
      int imagInt = 
                 (int)(zeroImagData[cnt]*unitCircleRadius);
      //Draw the pair of conjugate zeros.
      g.drawOval(realInt-2,imagInt-2,4,4);
      g.drawOval(realInt-2,-imagInt-2,4,4);
    }//end for loop

  }//end overridden paint method
}//end inner class ZPlane
//=======================================================//

}//end class InputGUI

Listing 19


Copyright 2006, Richard G. Baldwin.  Reproduction in whole or in part in any form or medium without express written permission from Richard Baldwin is prohibited.

About the author

Richard Baldwin is a college professor (at Austin Community College in Austin, TX) and private consultant whose primary focus is a combination of Java, C#, and XML. In addition to the many platform and/or language independent benefits of Java and C# applications, he believes that a combination of Java, C#, and XML will become the primary driving force in the delivery of structured information on the Web.

Richard has participated in numerous consulting projects and he frequently provides onsite training at the high-tech companies located in and around Austin, Texas.  He is the author of Baldwin's Programming Tutorials, which have gained a worldwide following among experienced and aspiring programmers. He has also published articles in JavaPro magazine.

In addition to his programming expertise, Richard has many years of practical experience in Digital Signal Processing (DSP).  His first job after he earned his Bachelor's degree was doing DSP in the Seismic Research Department of Texas Instruments.  (TI is still a world leader in DSP.)  In the following years, he applied his programming and DSP expertise to other interesting areas including sonar and underwater acoustics.

Richard holds an MSEE degree from Southern Methodist University and has many years of experience in the application of computer technology to real-world problems.

Baldwin@DickBaldwin.com






Comment and Contribute

 


(Maximum characters: 1200). You have characters left.

 

 


Sitemap | Contact Us

Rocket Fuel