# SOS2CAS

## Purpose:

Converts second order section form filter coefficients to cascade coefficients.

## Syntax:

SOS2CAS(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 series, the coefficients in 2nd order cascade form.

## Example:

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

c = sos2cas(sos, 1.0);

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

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

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

## Example:

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

{1,
0, 0, 1, 0.254856,
0}};

gain = 1.0;

c = sos2cas(sos, gain);

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

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

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

## Remarks:

SOS2CAS converts second order section form filter coefficients to cascade
form. Both forms 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 SOS form is an *N*x6 array:

**{{b**_{10},
b_{11},
b_{12},
1.0, a_{11},
a_{12}},

_{ }{b_{20},
b_{21},
b_{22},
1.0, a_{21},
a_{22}},

...

** {b**_{N0},
b_{N1},
b_{N2},
1.0, a_{N1},
a_{N2}}}

Each row of the SOS coefficients represents a second order 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}}

See CAS2SOS
to convert cascade form coefficients to second order section form.

## See Also:

CAS2SOS

CAS2TF

CAS2ZP

CASCADE

DADiSP/Filters

SOS2TF

SOS2ZP

SOSFILT

TF2CAS

TF2ZP

TF2ZPK

ZFREQ