sos2ss

Convert digital filter second-order section parameters to state-space form

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Syntax

[A,B,C,D] = sos2ss(sos)
[A,B,C,D] = sos2ss(sos,g)

Description

sos2ss converts a second-order section representation of a digital filter to an equivalent state-space representation.

[A,B,C,D] = sos2ss(sos) converts sos, a system expressed in second-order section form, to a single-input, single-output state-space representation:

x(n+1)=Ax(n)+Bu(n),y(n)=Cx(n)+Du(n).

The discrete transfer function in second-order section form is given by

H(z)=∏k=1LHk(z)=∏k=1Lb0k+b1kz−1+b2kz−21+a1kz−1+a2kz−2.

sos is a L × 6 matrix organized as

sos=[b01b11b211a11a21b02b12b221a12a22⋮⋮⋮⋮⋮⋮b0Lb1Lb2L1a1La2L].

The entries of sos must be real for proper conversion to state space. The returned matrix A is of size 2L × 2L, B is a 2L × 1 column vector, C is a 1 × 2L row vector, and D is a 1 × 1 scalar.

[A,B,C,D] = sos2ss(sos,g) converts to state space a system sos in second-order section form with gain g:

H(z)=g∏k=1LHk(z).

Examples

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Open Live Script

Compute the state-space representation of a simple second-order section system with a gain of 2.

sos = [1  1  1  1   0  -1 ;
      -2  3  1  1  10   1];
[A,B,C,D] = sos2ss(sos,2)
A = 4×4

   -10     0    10     1
     1     0     0     0
     0     1     0     0
     0     0     1     0


B = 4×1

     1
     0
     0
     0


C = 1×4

    42     4   -32    -2


D = -4

Algorithms

sos2ss first converts from second-order sections to transfer function using sos2tf, and then from transfer function to state-space using tf2ss.

See Also

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Introduced before R2006a

Signal Processing Toolbox Documentation

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