# CAS2ZP

## Purpose:

Converts cascade form filter coefficients to zeros, poles and gain.

## Syntax:

CAS2ZP(c)

(z, p, k) = CAS2ZP(c)

c |
- |
A series. The filter coefficients
in cascade form. |

## Returns:

A Nx3 array where the first column contains the zeros, the second column
contains the poles and the third column contains the gain.

**(z, p, k) = CAS2ZP(c)** returns
the zeros, poles and gain as three separate arrays.

## Example:

c = {1, 1, -2, 0, -0.7, 0.1};

W1: cas2zp({1, 1, -2, 0, -0.7, 0.1})

W1 == {{0.0, 0.5, 1.0},

{2.0,
0.2}}

The 2nd order cascade filter coefficients represent the following Z
transform:

The first column of W1 contains the zeros, the second column contains
the poles and the third column is the gain.

## Example:

c = {1, 1, -2, 0, -0.7, 0.1};

(z, p, k) = cas2zp(c);

z == {0.0, 2.0};

p == {0.5, 0.2};

k == 1.0;

The 2nd order cascade filter coefficients represent the following Z
transform:

Same as the previous example except **z**
contains the zeros, **p** contains
the poles and **k** is the gain of
the system.

## Remarks:

CAS2ZP converts cascade coefficients to zeros, poles and gain of a discrete
system where the input coefficients represent the following Z transform:

or:

where *G*
is the system gain, *b*_{k}
and *a*_{k} are the filter
coefficients for the *k*^{th}
stage.

The cascade filter coefficients are returned
as a single column series with the coefficients in the following order:

{G, b_{10}, b_{11}, b_{12},
a_{11}, a_{12}, b_{20}, b_{21}, b_{22},
a_{21}, a_{22}, ... , b_{N0}, b_{N1},
b_{N2}, a_{N1}, a_{N2}}

CAS2ZP also works for analog cascade coefficients. In this case, the
cascade system function becomes:

or equivalently:

See ZP2CAS to convert zeros, poles
and gain to cascade form.

## See Also:

CAS2SOS

CAS2TF

CASCADE

DADiSP/Filters

RESIDUEZ

TF2CAS

TF2ZP

TF2ZPK

ZFREQ

ZP2CAS