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# IIR Filters

DOI link for IIR Filters

IIR Filters book

# IIR Filters

DOI link for IIR Filters

IIR Filters book

## ABSTRACT

A digital filter with impulse response having infinite length (i.e., its values outside any finite interval cannot all be zero) is termed infinite impulse response (IIR) filter. The most important class of IIR filters can be described by the difference equation

(19.1)

where x(n) is the input, y(n) is the output of the filter, {a1, a2, …, aN}, and {b0, b1, …, bM} are the filter coefficients. We assume that aN ≠ 0. The impulse response is the output of the system when it is driven by a unit impulse at n = 0, with the system being initially at rest, i.e., the output being zero prior to applying the input. We denote the impulse response by h(n). With x(0) = 1, x(n) = 0, for n ≠ 0, and y(n) = 0 for n < 0, we can compute h(n), n ≤ 0, from (19.1) in a recursive manner.