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.

See Also:

CAS2SOS

CAS2TF

CASCADE

DADiSP/Filters

RESIDUEZ

SOS2CAS

SOS2TF

SOSFILT

TF2CAS

TF2ZP

TF2ZPK

ZFREQ

ZP2CAS

ZP2SOS