Infinite Impulse Response Filters, Introduction.

Cuthbert Nyack
An infinite impulse response filter(IIR) is one whose impulse response goes on forever. Recursive filters are closely associated with IIR filters but are not exclusively IIR. The transfer function of an IIR filter is shown below. For it to be IIR, at least one of the a's in the denominator must be non zero. M, the number of zeros should be less than N, the number of poles.
To obtain the frequency response of the filter, substitute the following relation between z and omega. T is the sampling time.
This results in a Frequency response with the general form.
To obtain the time sequence of the output or the impulse response use the following equivalent difference equation.

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COPYRIGHT © 1999 Cuthbert A. Nyack.