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Matlab Direct-Form to State-Space Conversion

Matlab and Octave support state-space models with functions such as

Note that while these utilities are documented primarily for use with continuous-time systems, they are also used for discrete-time systems.

Let's repeat the previous example using Matlab:

>> num = [1 2 3]; % transfer function numerator 
>> den = [1 1/2 1/3]; % denominator coefficients
>> [A,B,C,D] = tf2ss(num,den)

A =
   -0.5000   -0.3333
    1.0000         0

B =
     1
     0

C =  1.5000    2.6667

D =  1

>> [N,D] = ss2tf(A,B,C,D)

N = 1.0000    2.0000    3.0000

D = 1.0000    0.5000    0.3333

The tf2ss and ss2tf functions are documented online at The Mathworks help desk as well as within Matlab or Octave itself (say help tf2ss).


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``Introduction to Digital Filters with Audio Applications'', by Julius O. Smith III, (September 2007 Edition).
Copyright © 2021-11-22 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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