Non-symmetric Convex Polytope and Gabor Orthonormal Bases

TL;DR

This paper proves that non-symmetric convex polytopes cannot be used as window functions to generate Gabor orthonormal bases with any time-frequency set.

Contribution

It establishes a fundamental limitation on the use of non-symmetric convex polytopes in Gabor analysis.

Findings

Non-symmetric convex polytopes cannot serve as Gabor window functions.

Gabor orthonormal bases cannot be formed using non-symmetric convex polytopes.

Provides theoretical proof of the limitation.

Abstract

In this paper, we show that the non-symmetric convex polytope cannot be served as a window function to produce a Gabor orthonormal basis by any time-frequency sets.