Design of Tight Minimum-Sidelobe Windows by Riemannian Newton's Method

TL;DR

This paper introduces a Riemannian Newton's method to design tight windows with minimal sidelobe energy for the short-time Fourier transform, improving robustness in signal processing.

Contribution

It formulates the tight window design as a constrained spectral concentration problem and derives an efficient Riemannian Newton's method on an oblique manifold.

Findings

The proposed algorithm converges in only a few iterations.

Designed windows significantly reduce sidelobe energy.

Method enhances robustness of DGT-domain processing.

Abstract

The short-time Fourier transform (STFT), or the discrete Gabor transform (DGT), has been extensively used in signal analysis and processing. Their properties are characterized by a window function. For signal processing, designing a special window called tight window is important because it is known to make DGT-domain processing robust to error. In this paper, we propose a method of designing tight windows that minimize the sidelobe energy. It is formulated as a constrained spectral concentration problem, and a Newton's method on an oblique manifold is derived to efficiently obtain a solution. Our numerical example showed that the proposed algorithm requires only several iterations to reach a stationary point.