Converts second order section form filter coefficients to cascade coefficients.

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. |

A series, the coefficients in 2nd order cascade form.

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.

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.

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 Nx6 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.