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