SOS2CAS

Purpose:

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:

{{b₁₀, b₁₁, b₁₂, 1.0, a₁₁, a₁₂},

{b₂₀, b₂₁, b₂₂, 1.0, a₂₁, a₂₂},

...

{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, b₁₀, b₁₁, b₁₂, a₁₁, a₁₂, b₂₀, b₂₁, b₂₂, a₂₁, a₂₂, ... , b_N0, b_N1, b_N2, a_N1, a_N2}

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