ss

Convert digital filter to state-space representation

Syntax

[A,B,C,D] = ss(d)

Description

[A,B,C,D] = ss(d) converts a digital filter, d, to its state-space representation.

The state-space representation of a filter is given by

$$\begin{array}{c}x(k+1)=Ax(k)+Bu(k),\\ y(k)=Cx(k)+Du(k),\end{array}$$

where x is the state vector, u is the input vector, and y is the output vector.

Examples

State-Space Representation of a Lowpass IIR Filter

Design a lowpass IIR filter of order 6. Specify a normalized passband frequency of $$0.2\pi$$ rad/sample. Compute the state-space representation of the filter.

d = designfilt('lowpassiir','FilterOrder',6,'PassbandFrequency',0.2);
[A,B,C,D] = ss(d)

A = 6×6

    1.5640   -0.9294         0         0         0         0
    1.0000         0         0         0         0         0
    0.1795    0.0036    1.6097   -0.8112         0         0
         0         0    1.0000         0         0         0
    0.0020    0.0000    0.0408    0.0021    1.6956   -0.7409
         0         0         0         0    1.0000         0

B = 6×1

    0.0913
         0
    0.0046
         0
    0.0001
         0

C = 1×6

    0.0020    0.0000    0.0408    0.0021    3.6956    0.2591

D = 5.2030e-05

Input Arguments

d — Digital filter

digitalFilter object

Digital filter, specified as a digitalFilter object. Use designfilt to generate a digital filter based on frequency-response specifications.

Example: d = designfilt('lowpassiir','FilterOrder',3,'HalfPowerFrequency',0.5) specifies a third-order Butterworth filter with normalized 3 dB frequency 0.5π rad/sample.

Output Arguments

A — State matrix

matrix

State matrix, returned as a matrix.

Data Types: double

B — Input-to-state matrix

matrix

Input-to-state matrix, returned as a matrix.

Data Types: double

C — State-to-output matrix

matrix

State-to-output matrix, returned as a matrix.

Data Types: double

D — Feedthrough matrix

matrix

Feedthrough matrix, returned as a matrix.

Data Types: double