# ZPLANE

## Purpose:

Displays a Pole-Zero plot of a Z-transform.

## Syntax:

ZPLANE(b, a)

 b - A series. The numerator (i.e. zero) coefficients in ascending powers of z-1. a - A series. The denominator (i.e. pole) coefficients in ascending powers of z-1.

## Alternate Syntax:

ZPLANE(z, p, g)

 z - A series. The zeros of the Z-transform. p - A series. The poles of the Z-transform. g - A scalar. The gain of the system.

## Alternate Syntax:

ZPLANE(c)

 c - A series. The system coefficients in cascaded biquad form. If c contains 2 columns, the coefficients are assumed to be in direct form, where the first column is b and the second column is a.

## Returns:

An XY series, where each pole is plotted as a light red "x" and each zero is plotted as a black "o". The unit circle is displayed as a solid circle.

## Example: W1: zplane({1}, {1, -0.5}) Displays the unit circle with a single pole at z = 0.5. The input is given as a system function in ascending terms of z-1.

## Example: z = roots({1, -2, 0})

p = roots({1, -0.7, 0.1})

zplane(z, p, 1) Displays two real poles and two zeros in the current Window. This is equivalent to:

zplane({1, -2, 0}, {1, -0.7, 0.1})

## Remarks:

For zplane(b, a), the input series represent the terms of the rational polynomial H(z) = b(z) / a(z) where: z = e jω complex frequency N = number of numerator terms M = number of denominator terms

For zplane(z, p, g), the gain term must be present, but it does not effect the resulting plot.

For zplane(c), the input c is assumed to be a single column of coefficients in cascaded bi-quad form. This is the output format of IIR filters designed by DADiSP/Filters and processed by the CASCADE function. or equivalently: where G is the system gain, bk and ak are the filter coefficients for the kth stage.

If c contains 2 columns, the coefficients are assumed to be in direct form, where the first column is b and the second column is a.

The aspect ratio of the window is set to square to preserve a circular unit circle.

Each pole is plotted as a light red "x" and each zero as a black "o". The unit circle is displayed as a solid circle in the current series color. Axes lines are also drawn through the origin.

Multiple zeros and poles are labeled with a multiplicity number to the upper right of the symbol.

See SPLANE for a Pole-Zero plot of a continuous system.

FILTEQ

GIMPULSE

GRPDELAY

IMPZ

RESIDUEZ

ROOTS

SPLANE

TF2ZPK

ZFREQ