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, bk and ak are the filter coefficients for the kth stage.

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

 

{G, b10, b11, b12, a11, a12, b20, b21, b22, a21, a22, ... , bN0, bN1, bN2, aN1, aN2}

 

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