A rational-expansion-based method to compute Gabor coefficients of 2D indicator functions supported on polygonal domain

Ligang Sun, Roeland J. Dilz and Martijn C. van Beurden

Mathematics and Computers in Simulation (MATCOM), 2023, vol. 206, issue C, 487-502

Abstract: We propose a method to compute Gabor coefficients of a two-dimensional (2D) indicator function supported on a polygonal domain by means of rational expansion of the Faddeeva function and by solving second-order linear difference equations. This method has the following three attractive features: (1) the problem of computing Gabor coefficients is formulated as the calculation of a sequence of integrals with a uniform structure, (2) a rational expansion based on fast Fourier transform (FFT) is used to approximate the Faddeeva function on the entire complex plane, (3) second-order inhomogeneous linear difference equations are derived for previous integrals and they are solved stably with Olver’s algorithm. Numerical quadrature to compute Gabor coefficients is avoided. Numerical examples show this rational-expansion-based method significantly outperforms numerical quadrature in terms of computation time while maintaining accuracy.

Keywords: Gabor coefficient; Faddeeva function; Rational expansion; Second-order difference equation; Olver’s algorithm (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:206:y:2023:i:c:p:487-502

DOI: 10.1016/j.matcom.2022.12.004

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