TF2SOS

Purpose:

Converts transfer function form filter coefficients to second order section form.

Syntax:

TF2SOS(b, a)

(sos, gain) = TF2SOS(b, a)

b	-	A series. The numerator (i.e. zero) coefficients in ascending powers of z^-1.
a	-	A series. The denominator (i.e. pole) coefficients in ascending powers of z^-1.

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) = TF2SOS(b, a) returns the Nx6 second order stages and gain in two separate variables.

Example:

b = {1};

a = {1, -0.5, 0.2};

sos = tf2sos(b, a);

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

The direct form filter coefficients represent the following Z transform:

The resulting 2nd order section coefficients represent the equivalent Z transform:

Since the original coefficients represent a single 2nd order system, the SOS denominator coefficients are identical.

Example:

b = {1};

a = {1, -0.5, 0.2, 0.1};

(sos, gain) = tf2sos(b, a);

sos == {{1, 0, 0, 1, -0.754856, 0.392379},

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

gain == 1

The direct form filter coefficients represent the following Z transform:

The resulting SOS coefficients represent the equivalent Z transform:

The direct form coefficients are represented by two stages of SOS coefficients.

Remarks:

TF2SOS converts direct form filter coefficients to second order section form. The direct form coefficients represent the terms of the rational polynomial H(z) = b(z) / a(z) where:

$image\zplane03.gif$

z	=	e^jω complex frequency
N	=	number of numerator terms
M	=	number of denominator terms

The second order section form of the coefficients represent the equivalent 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.

See SOS2TF to convert second order section form coefficients to direct form.

TF2SOS

Purpose:

Syntax:

Returns:

Example:

Example:

Remarks:

See Also: