An Efficient Method of Group Delay Equalization for Digital IIR Filters

Abstract

The paper presents the equalization problem of non-linear phase response of digital IIR type filters. An improved analytical method of designing a low-order equalizer is presented. The proposed approach is compared with the original method. The genetic algorithm is presented as an iterative method of optimization. The vector and matrix representation of the all-pass equalizer are shown and introduced to the algorithm. The results are compared with the analytical method. In this paper we have also proposed the use of an aging factor and setting the initial population of the genetic algorithm around the solution provided by the analytical methodology.

A graphical user interface for designing time-varying IIR filters with equalized group delay

“…This fact can be a serious problem for acquiring a precise measurement. In [1], [2] we have proposed few methodologies to design a proper allpass based equaliser to deal with the non-constant group delay which are also added to our system. Fig.…”

“…The Taylor expansion methodology [1] is a very efficient tool if the initial difference between minimum and maximum value of the nonconstant group delay in the passband is not too significant. The analytical pole plamement method [2] is efficient if the needed order of the equaliser is between 4th and 8th. What is more, if the analytical solutions cannot provide satisfactory outcome, one can turn to the iterative methods provided by Matlab or by our modified genetic algorithm [2].…”

“…The analytical pole plamement method [2] is efficient if the needed order of the equaliser is between 4th and 8th. What is more, if the analytical solutions cannot provide satisfactory outcome, one can turn to the iterative methods provided by Matlab or by our modified genetic algorithm [2]. Of course, the user can also import allpass based equaliser from Matlab workspace obtained by any other method.…”

“…The user can decide whether the optimisation should start around the shape he/she chose or should there be no a priori input. We have also implemented the aging factor described in [2] that allows the mutation process to increase its probability and boundaries. The last but not least improvement is the possibility of using the GPU power to compute the optimal variation function.…”

“…Such design is characterised by non-constant group delay response (nonlinear phase response). In [1], [2] we have proposed analytical and iterative methods of designing group delay equalisers based on the allpass filter to minimize this problem. Unfortunately, by adding the equaliser in line the time domain characteristic gets affected.…”