IEEE Access (Jan 2021)
Infinite Impulse Response Filter Bank Based Graphic Equalizer Design via Functional Inequality Constrained Optimization and Genetic Algorithm
Abstract
It is worth noting that a graphical equalizer is a linear time-invariant system. Hence, its input-output relationship can be modeled by a transfer function. The graphical equalizer is realized by a parallel connection of a set of filters called a filter bank. Each filter in the filter bank is designed to equalize a certain frequency band of the audio signal. There are two types of graphic equalizers. The first type of graphical equalizers is based on a finite impulse response (FIR) filter bank. However, it requires very high order FIR filters to achieve a certain degree of equalization precision. As a result, the required computational power is very high. Also, the output of the graphical equalizer is suffered from a very long time delay. The second type of graphical equalizers is based on an infinite impulse response (IIR) filter bank. It can address the above issues. That is, its implementation cost is low. To design each IIR filter, the total absolute error between the ideal equalization and the actual equalization in the passband of the IIR filter is minimized subject to the constraints imposed on the stability criterion of the IIR filter as well as on the maximum modulus error between the ideal equalization and the actual equalization in the corresponding passband. This design problem is a functional inequality constrained optimization problem which consists of an infinite number of inequality constraints. By performing the downsampling in the frequency domain, the infinite constrained optimization problem becomes the finite constrained optimization problem. By using the genetic algorithm to find the solution of this optimization problem, the coefficients of all the IIR filters are obtained. The computer numerical simulation results show that the equalizer designed by our proposed method yields a good equalization performance.
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