Abstract
Design of full-band infinite impulse response (IIR) digital differentiator (DD) and digital integrator (DI) based on the L<sub>k</sub>-norm and the min-max optimality criteria have been demonstrated in literature. However, the designed IIR DDs and DIs using these criteria do not have linear phase or have unsatisfactory magnitude response. In this paper, a novel approach to design, optimize and improve the magnitude response and the linearity of the phase response of IIR DD and DI using the cuckoo search (CS) optimization algorithm is proposed. The proposed approach is based on a varied L<sub><i>k</i></sub>-norm where <inline-formula> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula> linearly increases with the number of the frequency samples between the values 1 and 2. The design and optimization of DDs and DIs are carried out using the CS optimization method due to its simplicity, efficiency, and robustness in solving general multidimensional optimization problems. The performance of the designed DDs and DIs using the proposed approach is compared with designs based on different criteria and algorithms available in literature. The comparison shows that the designed DDs and DIs based on the proposed approach have better phase responses and better or at least comparable magnitude responses compared to those of DDs and DIs designed using other methods in the literature.
Highlights
Digital differentiator (DD) and digital integrator (DI) have been used in many engineering applications [1-5]
The stability requirement of any digital system makes the design of infinite impulse response (IIR) digital system more difficult compared to finite impulse response (FIR) digital system
DESIGN EXAMPLES AND DISCUSSION we present the results of sample design examples of second, third and fourth order IIR DDs and DIs using the cuckoo search (CS) algorithm based on the proposed new objective function
Summary
Digital differentiator (DD) and digital integrator (DI) have been used in many engineering applications [1-5]. The use of evolutionary and swarm intelligence algorithms to design and optimize the performance of DDs and DIs has been reported in [17-26]. The designed IIR DDs and DIs in [17-19, 21-23, 25-26] do not have linear phase over the entire frequency band and their magnitude response can be further optimized to improve the overall performance. The main purpose of this paper is to report a new approach and extend our work in [49-53] and explore the performance of the CS algorithm in the design and optimization of IIR DDs and DIs in comparison with other methods. The performance of the designed DD and DI is improved by introducing a new objective function combined with using the powerful CS algorithm to search for the DD and DI parameters that result in the optimal design.
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