Using PEZ: Add & Weight Functions

Add Overview

The ADD pole/zero options are fairly simple. In general, you click on either the add pole or zero button, move the mouse over to the Z-plane, and then click the destination of where you want to place pole or zero. If you change your mind and decide that you do not want to add a pole or zero, simply click the mouse outside of the Z-plane (but still in the main control window), and PEZ will take you out of the add mode.

When you are adding a pole or zero, PEZ uses the Weight value to determine how many poles or zeros are added to the Z-Plane. If you add poles or zeros on top of existing poles or zeros, PEZ does all of the nasty work of analyzing the situation and makes the right changes. For example, if you have a current weight of 4, and add a pole on top of a location that already has 2 zeros, PEZ will remove the two zeros and replace them with 2 poles.

Additionally, PEZ is configured to represent REAL systems. This means that if you have a pole or zero with an imaginary component, PEZ will automatically add the complex conjugate. This results in a mirroring across the real (or X) axis.

The Different ADD Options:

Add Single Weighted:

This option allows you to add a single weighted pole or zero. The new addition is (as with all objects) mirrored across the real axis.

Add Multiple Weighted:

This option allows you to add a several weighted poles or zeros. It is in effect the same as repeating the Add Single option several times until the user clicks outside the bounds of the Z-Axis.

Add Double:

These options are built for adding poles and zeros with mirrors about the unit circle. For example, clicking on a Add Double Pole, and clicking close to the unit circle (on the inner side) can result in a plot such as:

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For the Double Add Pole/Zero Combo, An operation similar to an add double is performed, but this time a pole is placed inside the unit circle, and a zero is mirrored outside of the unit circle. It does not matter whether you click inside or outside of the unit circle, PEZ will figure out where to place what for you, such as this Double Pole/Zero Combo Add:

Changing The Weight:

For the Add and Delete options of PEZ, a Weight control box is added to allow easier manipulations of weighted poles or zeros. Basically, whenever there is an Add or Delete operation, PEZ uses the Current Weight value to determine how many objects should be placed or removed from the current location.

For example, if you wanted to insert a delay of 5 in the impulse response, you would want to add 5 poles at the origin of the Z-plane. Rather than adding the 5 poles by hand, you could change the current weight to 5, then add a single pole at the origin. A small number 5 will be placed next to your new pole to signify that there are 5 poles for the one pole marking in the Z-Plane.

PEZ maintains a list of how many of what are where, and maintains the list to reflect changes in the filter.