# Documentation

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# ss

Convert digital filter to state-space representation

## Description

example

[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

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

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

## Examples

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Design a lowpass IIR filter of order 6. Specify a normalized passband frequency of 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 =

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 =

0.0913
0
0.0046
0
0.0001
0

C =

0.0020    0.0000    0.0408    0.0021    3.6956    0.2591

D =

5.2030e-05

## Input Arguments

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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

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State matrix, returned as a matrix.

Data Types: double

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

Data Types: double

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

Data Types: double

Feedthrough matrix, returned as a matrix.

Data Types: double