An Analysis of Linear Phase IIR Filters and a Condition for Perfect Linear Phase

概要

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A technique for realizing linear phase IIR filters has proposed by Powell and Chau, which gives real time realization of H(z^<-1>)・H(z) where H(z) is a causal nonlinear phase IIR filter. The technique is based on approximating the infinite impulse response of H(z) to a finite length one. In the system, the input sequence is time reversed on block by block basis and section-convolved with H(z) to realize a real time recursive implementation of the noncausal transfer function H(z^<-1>). After time reversed again, the sequence passes through another filter with H(z), giving the desired linear phase filtered sequence. Being disappointed our expectation, the group delay response of the system has a minor amplitude, short period sinusoidal oscillation superimposed on a constant value. In image processing or transmission applications, the oscillation seriously degrades the image quality. To overcome this difficulty, the system in time domain with state space representation is analyzed, and a condition that the system has perfect linear phase characteristic and to be time-invariant, is shown.
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