7 - Infinite impulse response (IIR) filter design

Abstract

Infinite impulse response (IIR) filters have impulse responses that are infinite in duration. This is in contrast with the impulse responses of finite impulse response (FIR) filters, which are non-zero for only a finite number of samples. Since the IIR filter is a linear system, the output and input are related by the convolution sum. Unlike the FIR filter, exact linear phase is impossible to achieve using an IIR filter. This is because exact linear phase implies that the filter impulse response must be symmetric. From the input/output relation of the IIR filter, it can be observed that it is impossible to have an impulse response that is zero for k<0 and non-zero for k from zero to infinity. However, near-linear phase IIR filters do exist. As IIR filters cannot have exact linear phase, its design is therefore more complex. Most of the common design techniques assume that the phase response is not important and only approximate the magnitude response. If phase response is not important, then for the same magnitude response specifications, the required order for IIR filter is normally lower than that required for FIR filters. This is a definite advantage as a lower order implies a lower computational cost and a shorter delay.