Design of Infinite Impulse Response Filter Using Fractional Derivative Constraints and Hybrid Particle Swarm Optimizatio
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Design of Infinite Impulse Response Filter Using Fractional Derivative Constraints and Hybrid Particle Swarm Optimization N. Agrawal1 · A. Kumar2 · Varun Bajaj2 Received: 15 March 2019 / Revised: 12 May 2020 / Accepted: 13 May 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract In this paper, a new method for designing digital infinite impulse response filter with nearly linear-phase response is presented using fractional derivative constraints (FDC). The design problem is constructed as a phase optimization problem between the desired and designed phase response of a filter. In order to achieve the highly accurate passband (pb) response, phase response is fitted to desired response more precisely using FDC, due to which design problem becomes a multimodal error surface that is constructed from sum of passband error (ep) and stopband error (es). Optimal value of FDC is accomplished by minimizing the total error (er0) using improved swarm-based optimization technique, which is formulated by associating the scout bee mechanism of artificial bee colony algorithm with particle swarm optimization and termed as hybrid particle swarm optimization. The simulated results reflect that the improved response in passband along with better transition width is achieved using the proposed method. It is observed that about 90–99% of improvement in passband error can be achieved with 100% reduction in maximum passband ripple. However, slight reduction in stopband attenuation (As), in some cases, results within the permissible limit. The designed filters using this method are also stable toward finite word length effect. Keywords Fractional derivatives (FD) · IIR filter · Linear phase · Evolutionary technique (ET) · Hybrid PSO
1 Introduction The designing of digital infinite impulse response (IIR) filter has been extensively practiced due to low computational requirement as compared to finite impulse response (FIR) filters. They are used in several applications such as notch filtering * N. Agrawal [email protected] Extended author information available on the last page of the article Vol.:(0123456789)
Circuits, Systems, and Signal Processing
[46], fractional delay filtering [45], phase splitters, Hilbert transformers [18], multirate filterbank [29]. All these applications rely on efficient design of IIR filters. Therefore, in the early stage of research, several attempts were made to propose the improved design of IIR filters [7, 11, 28, 32, 35]. These methods involve conventional closed-form technique, in which an equivalent analog filter is translated into digital via a suitable approximation. However, the filters designed using these methods are more susceptible to quantization and truncation noise and also have nonlinear phase response [41]. The deviation of filter response due to realization of filter by quantizing its filter tap values with finite number of bits leads to quantization and truncation error, also termed as word length effect, which is a count of binary bits used f
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