# SOS2ZP

## Purpose:

Converts second order section form filter coefficients to zeros, poles and gain.

## Syntax:

SOS2ZP(sos, g)

(z, p, k) = SOS2ZP(sos, g)

 sos - A Nx6 array where the first 3 columns are the numerator terms and the last 3 columns are the denominator terms. Each row represents a 2nd order stage. g - Optional. A real, the system gain. Defaults to 1.0.

## 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) = SOS2ZP(sos, g) returns the zeros, poles and gain as three separate arrays.

## Example:

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

(z, p, k) = sos2zp(sos);

z = {0.0, 2.0};

p = {0.5, 0.2};

k = 1.0;

The 2nd order section filter coefficients represent the following Z transform: z contains the zeros, p contains the poles and k is the gain of the system.

## Remarks:

SOS2ZP converts second order section 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 SOS form is an Nx6 array:

{{b10,  b11,  b12,  1.0,  a11,  a12},

{b20,  b21,  b22,  1.0,  a21,  a22},

...

{bN0,  bN1,  bN2,  1.0,  aN1,  aN2}}

Each row of the SOS coefficients represents a second order stage.

SOS2ZP also works for analog cascade coefficients. In this case, the cascade system function becomes: or equivalently: See ZP2SOS to convert zeros, poles and gain to SOS form.

CAS2SOS

CAS2TF

RESIDUEZ

SOS2CAS

SOS2TF

SOSFILT

TF2CAS

TF2ZP

TF2ZPK

ZFREQ

ZP2CAS

ZP2SOS