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

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. • We propose a method to compute Gabor coefficient of a 2D indicator function. • Gabor coefficient is formulated into a sequence of integrals with uniform structure. • Difference equation is derived based on rational expansion of the Faddeeva function. • The proposed method significantly reduces computation time while keeping accuracy. [ABSTRACT FROM AUTHOR]