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:

image\zplane01.gif

 

W1: zplane({1}, {1, -0.5})

 

image\zplane1pic.gif

 

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:

image\zplane02.gif

 

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

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

zplane(z, p, 1)

 

image\zplane2pic.gif

 

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:

 

image\zplane03.gif

 

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.

See Also:

CASCADE

DADiSP/Filters

FILTEQ

GIMPULSE

GRPDELAY

IMPZ

RESIDUEZ

ROOTS

SPLANE

TF2ZPK

ZFREQ