NDLI: Optimal design of L 1-norm based IIR digital differentiators and integrators using the bat algorithm

Content Provider	IET Digital Library
Author	Aggarwal, Apoorva Rawat, Tarun K. Upadhyay, Dharmendra K.
Abstract	In this study, new infinite impulse response (IIR) digital differentiators of second, third and fourth orders based on optimising the L 1-error fitness function using the bat algorithm (BA) are proposed. The coefficients of numerator and denominator of the differentiators are computed by minimising the L 1-norm of the error fitness function along with imposing the constraint for the location of poles and zeros within the unit circle to ensure minimum phase. The transfer function of the differentiators are inverted and transformed into the digital integrators of the same orders. The results obtained for the solutions by the proposed L 1-based BA (L 1-BA) are superior to the designs using other techniques such as particle swarm optimisation and real-coded genetic algorithm. The designed optimal differentiator and integrator are compared with the existing models and are found to be of high accuracy and flatness in a wide frequency range along with minimum absolute magnitude error. The mean relative error (dB) is obtained as low as −67 dB and −73 dB for the proposed differentiators and integrators, respectively.
Starting Page	26
Ending Page	35
Page Count	10
ISSN	17519675
Volume Number	11
e-ISSN	17519683
Issue Number	Issue 1, Feb (2017)
Alternate Webpage(s)	https://digital-library.theiet.org/content/journals/iet-spr/11/1
Alternate Webpage(s)	https://digital-library.theiet.org/content/journals/10.1049/iet-spr.2016.0010
Journal	IET Signal Processing
Publisher Date	2016-07-21
Access Restriction	Open
Rights Holder	© The Institution of Engineering and Technology
Subject Keyword	Bat Algorithm Differentiator Denominator Differentiator Numerator Differentiator Transfer Function Error Fitness Function Filtering Method in Signal Processing Genetic Algorithm IIR Digital Differentiators IIR Filter Infinite Impulse Response Integrators L1-error Fitness Function L1-norm Minimization Minimisation Minimum Absolute Magnitude Error Optimal Design Optimisation Technique Particle Swarm Optimisation Pole-and-zero Location Poles And Zeros Real-coded Genetic Algorithm Signal Processing Theory Transfer Function
Content Type	Text
Resource Type	Article
Subject	Signal Processing Electrical and Electronic Engineering

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