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.
| Original language | English |
|---|---|
| Pages (from-to) | 487-502 |
| Number of pages | 16 |
| Journal | Mathematics and Computers in Simulation |
| Volume | 206 |
| DOIs | |
| Publication status | Published - 1 Apr 2023 |
Funding
This work was funded by NWO-TTW, The Netherlands as part of the HTSM program under project number 16184. L. Sun is grateful to J. A. C. Weideman from Stellenbosch University for his support. The authors also thank H. G. Feichtinger for his contributions to the contents of this paper.
| Funders | Funder number |
|---|---|
| Netherlands Organisation for Applied Scientific Research | 16184 |
| University of Stellenbosch |
Keywords
- Gabor coefficient
- Faddeeva function
- Rational expansion
- Second-order difference equation
- Olver’s algorithm
- Olver's algorithm