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sos2ss

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

Syntax

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

Description

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

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

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

sos is a L-by-6 matrix organized as

The entries of sos must be real for proper conversion to state space. The returned matrix A is size N-by-N, where N = L− B is a length N−1 column vector, C is a length N−1 row vector, and D is a scalar.

[A,B,C,D] = sos2ss(sos,g) converts the system sos in second-order section form with gain g.

Examples

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State-Space Representation of a Second-Order Section System

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)
A =

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


B =

     1
     0
     0
     0


C =

    21     2   -16    -1


D =

    -2

More About

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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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