CAS2SOS

Purpose:

Converts cascade form filter coefficients to second order section form.

Syntax:

CAS2SOS(c)

(sos, gain) = CAS2SOS(c)

c

-

A series. The filter coefficients in cascade form.

Returns:

An Nx6 column series, where the first 3 columns contain the numerator coefficients and the last three columns contain the denominator coefficients. Each row represents a 2nd order stage.

 

(sos, gain) = CAS2SOS(c) returns the Nx6 second order stages and gain in two separate variables.

Example:

c = {1, 1, 0, 0, -0.5, 0.2};

(sos, gain) = cas2sos(c);

 

sos == {{1, 0, 0, 1, -0.5, 0.2}

gain == 1.0

 

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

 

 

The resulting SOS form filter coefficients represent the same Z transform.

Example:

c = {1, 1, 0, 0, -0.754856, 0.392379, 1, 0, 0, 0.254856, 0};

(sos, gain) = cas2dir(c);

 

sos == {{1, 0, 0, 1, -0.754856, 0.292379},

        {1, 0, 0, 1,  0.254856, 0}}

 

gain == 1.0

 

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

 

 

The resulting SOS form filter coefficients represent the same Z transform.

Remarks:

CAS2SOS converts cascade form filter coefficients to second order section form. Both forms 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}

 

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.

 

If the gain is not returned as a separate variable, the gain is embedded into the first stage.

 

See SOS2CAS to convert SOS form coefficients to cascade form.

See Also:

CAS2TF

CAS2ZP

DADiSP/Filters

SOS2CAS

SOSFILT

TF2CAS

TF2ZP

TF2ZPK

ZFREQ