A novel approach to design optimal 2-D digital differentiator using vortex search optimization algorithm
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A novel approach to design optimal 2-D digital differentiator using vortex search optimization algorithm Suman Yadav 1,2 & Richa Yadav 2 & Ashwni Kumar 2 & Manjeet Kumar 3 Received: 22 June 2020 / Revised: 8 September 2020 / Accepted: 15 September 2020 # Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract
The designing of 2-D digital differentiator is multimodal and high dimensional problem which requires large number of differentiator coefficients to be optimized, hence conventional design techniques will not lead to optimal 2-D differentiator design. Metaheuristic approaches is a good approach to handle multimodal and high dimensional problem under consideration. In this paper, a novel method for the design of FIR two-dimensional (2-D) digital differentiator with quadrantally odd symmetric properties is proposed. The coefficients of 2-D digital differentiator are computed and optimized using vortex search optimization (VSO) algorithm with the support of L1 error objective function. The unique combination of VSO and L1 error fitness function aids in achieving flatter magnitude response in designing of 2-D differentiator. Further, some comparative analysis with the well-known established techniques like cuckoo search algorithm (CSA), particle swarm optimization (PSO) and real coded genetic algorithm (RCGA) methodology is reported over full frequency bands, in order to demonstrate the advantage of the proposed novel 2-D digital differentiator design approach. To measure the performance of proposed system, some parameters are selected for illustration such as absolute magnitude error, mean absolute error, standard deviation and execution time. The excellence of the proposed approach is observed in approximating the ideal response of 2-D differentiator in contrast to other algorithms and to provide global optimal solution. Keywords Digital FIR 2-D differentiator . Vortex search algorithm . Optimization . Metaheuristic algorithm
1 Introduction Digital filters are extensively accepted in many applications due to their superior performance, less area requirement during implementation, ease in implementation with adaptive
* Manjeet Kumar [email protected] Extended author information available on the last page of the article
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programmability and exact reproduction capability. In past few decades extensive research is reported by practitioners in the area of designing and implementation of digital differentiator and integrator, due to their applications in various fields like signal processing for linear and nonlinear system identification [18, 35], digital image processing to extract edges in an image [25, 26, 32], biomedical signal processing to detect R-peaks in electrocardiogram (ECG) signal [19–21], control engineering for disturbance rejection [13], radar to measure position and acceleration [29] and many more. The main function of the differentiator is to determine the time derivative of a signal to extract information regarding rapid transients.
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