- First, determine the filter transfer function
. In the
example, the transfer function can be written, by
inspection, as
If , we must ``pull out'' the parallel delay-free path:

The same result is obtained using long or synthetic division

- Next, draw the strictly causal part in
*direct form II*, as shown below:

It is important that the filter representation be

*canonical with respect to delay*, i.e., the number of delay elements equals the order of the filter - Assign a state variable to the output of each delay element (see figure)
- Write down the state-space representation by inspection. (Try it
and compare to answer above.)

Download StateSpace.pdf

Download StateSpace_2up.pdf

Download StateSpace_4up.pdf

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Center for Computer Research in Music and Acoustics (CCRMA), Stanford University

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