Efficient Analysis and Synthesis Using a New Factorization of the Gabor Frame Matrix

作者：S. Moreno-Picot, F. J. Ferri, M. Arevalillo-Herráez, Wladimiro Dı́az-Villanueva · 发表于：IEEE Transactions on Signal Processing · 年份：2018 · DOI：10.1109/TSP.2018.2855643 · 被引用次数：6 · 研究领域：Computer Science

In this paper, we consider the case in which one needs to carry out Gabor analysis and synthesis on large signals using a short support analysis window and its corresponding, possibly longer canonical dual window, respectively. In this asymmetric context, we propose a novel factorization of the Gabor frame operator that exploits its strong and well-known structure and leads to a computational cost for synthesis, which is comparable to the one needed for short support analysis. The proposed factorization applies to any Gabor system with very mild conditions and leads to a potentially promising alternative to current synthesis algorithms in the case of short analysis windows whose support is slightly above the number of frequency channels.