Initial Solution for the Optimum Design Delay Equalizers

Abstract

A novel methodology for allocating the poles of a group delay equalizer is introduced, in order to be applied as the initial solution of an optimization procedure that searches for the optimum result. Any chosen cost function related to equalizer designs has several local minima, because of the large number of parameters and the high function complexity. The goal of the present paper is to avoid those local minima, and consequently improve the robustness and convergence rate of equalizer designs. The method is based on the allocation presented in [14], introducing a new consistent approach to allocate the radii of the poles, and implementing a change in the choice for the phase of the poles, and also, a new decision criterion for both strategies presented in [14]. Simulation results are also presented.

Optimum design of group delay equalizers

“…The technique can be immediately extended to bandpass, bandstop and highpass filters. The initial parameter estimates were obtained with the algorithm described in [17].…”

“…Since constrained optimization becomes highly nonlinear, genetic algorithms have also been applied for allpass equalizer design [18,19]. For improved robustness, some procedures search for the optimal location of the equalizer poles and zeros [14][15][16][17], restricting the poles' radii to be lower than 1, thereby assuring stability.…”

An Efficient Method of Group Delay Equalization for Digital IIR Filters

“…In our studies we concentrated on providing a characteristic with the lowest difference between the maximum and minimum value of the group delay in the equalized filter's pass-band. In [4] and [10] Petraglia and Quelhas approached this problem by combining analytical analysis with iterative optimization techniques. Our studies showed that in terms of low order (up to 8-th) analytical equalization their strategy can be improved by choosing a different methodology of calculating the all-pass equalizer.…”

“…The main idea of the method proposed in [4,10] was to analyze an equalized IIR filter on the z-plane. The outermost pair of poles was considered in terms of their angle and radius.…”

“…In our studies we come up with a new methodology of the pole placement that improves final group delay in terms of the difference between maximum and minimum values in the pass-band. We propose to alter the equations delivered by [4] and [10] with our solutions (6) - (9) and (11) - (14). The specific values of the coefficients were chosen based on the experimental tests and careful analysis of the all-pass filter behavior with different pole placement.…”