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)

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, b_k and a_k are the filter coefficients for the k^th 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.

ZPLANE

Purpose:

Syntax:

Alternate Syntax:

Alternate Syntax:

Returns:

Example:

Example:

Remarks:

See Also: