Efficient algorithms for discrete Gabor transforms on a nonseparable lattice

TL;DR

This paper introduces the most computationally efficient algorithms to date for discrete Gabor transforms on nonseparable lattices, along with optimized C implementations, advancing both theoretical understanding and practical application.

Contribution

It presents new algorithms with the lowest known complexity for nonseparable Gabor lattices and provides optimized, freely available C implementations.

Findings

New algorithms outperform existing methods in computational complexity.

Optimized C implementations demonstrate practical efficiency.

The paper offers a comprehensive survey of Gabor analysis techniques.

Abstract

The Discrete Gabor Transform (DGT) is the most commonly used transform for signal analysis and synthesis using a linear frequency scale. It turns out that the involved operators are rich in structure if one samples the discrete phase space on a subgroup. Most of the literature focuses on separable subgroups, in this paper we will survey existing methods for a generalization to arbitrary groups, as well as present an improvement on existing methods. Comparisons are made with respect to the computational complexity, and the running time of optimized implementations in the C programming language. The new algorithms have the lowest known computational complexity for nonseparable lattices and the implementations are freely available for download. By summarizing general background information on the state of the art, this article can also be seen as a research survey, sharing with the readers experience in the numerical work in Gabor analysis.