A technique to truncate IIR filter impulse response and its application to real-time implementation of linear-phase IIR filters

A technique for realizing linear-phase infinite impulse response (IIR) filters has been proposed by Powell and Chau (1991) and gives a real-time implementation of H(z-1)·H(z), where H(z) is a causal IIR filter function. In their system, the input signal is divided into L-sample sections, time-reversed, section convolved with H(z), and time-reversed again. The signal is then filtered by H(z) to give the system output with a processing delay of 3L+1 samples. However, the group delay response of the system exhibits a minor sinusoidal variation superimposed on some constant value. This variation will degrade image quality in image processing and signal quality in signal transmission applications. Furthermore, the output of the system contains harmonic distortion for a sinusoidal input. The main drawbacks of Powell and Chauʹs technique are the large processing delay of 3L+1 samples and the accompanying phase and harmonic distortions. A smaller processing delay increases the phase and harmonic distortions, yet the amplitude response remains acceptable. Previously, the present authors presented a method of reducing the processing delay by shortening the section length by an integer factor N using a structure with increased number of paths for the time-reversed signal. The authors consider how to reduce the phase and harmonic distortions. We examined the operation of the sectioned convolution and analyzed it based on a state-space representation. Then, we found that the cause of the distortions is a periodic variation of the impulse response length in the sectioned convolution. To overcome this problem, a technique is devised to realize a recursive circuit having a truncated impulse response with a fixed-length L. A system applying this technique to the Powell-Chau system is demonstrated to exhibit perfect linear-phase characteristic and produce virtually no harmonic distortion. Therefore, the section length L can be reduced without limitation due to phase and harmonic distortions. Two methods for reducing the increased computational complexity of this technique assuming fixed L are developed, and simulations are performed for the proposed system to confirm the expected improvements.