State Space Realization

Above, we used a matrix multiply to represent convolution of the
filter input signal with the filter's impulse response. This only
works for FIR filters since an IIR filter would require an infinite
impulse-response matrix. IIR filters have an extensively used matrix
representation called *state space models* (or ``realizations'').
They are especially convenient for representing filters with
*multiple inputs* and *multiple outputs* (MIMO filters).
An order digital filter with inputs and outputs can be written
in state-space form as follows:

where is the length

State-space models are described further in Appendix E. Here, we will only give an illustrative example and make a few observations:

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