Design of Tight Minimum-Sidelobe Windows by Riemannian Newton's Method
Signal Processing
2021-12-07 v2 Numerical Analysis
Audio and Speech Processing
Numerical Analysis
Optimization and Control
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.
Keywords
Cite
@article{arxiv.2111.01593,
title = {Design of Tight Minimum-Sidelobe Windows by Riemannian Newton's Method},
author = {Daichi Kitahara and Kohei Yatabe},
journal= {arXiv preprint arXiv:2111.01593},
year = {2021}
}