IIR Filter Design
In Chapter 4, we saw that the transfer function of a linear recursive or infinite impulse response (IIR) filter is a ratio of polynomials in z, rather than just a single polynomial that describes a finite impulse response (FIR) filter. The direct-form algorithm, transfer function, and gain of an IIR filter were given in (4.10) through (4.12):
Thus, the IIR transfer function has poles as well as (usually) zeros on the z-plane, and, as stated in (4.39), the poles must be inside the unit circle for stability. ...
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