时频分析的若干问题
The abstruse meets the applicable: Some aspects of time-frequency analysis
摘要：
与信号处理理论相联系的傅里叶分析领域在过去的二十年里经历了迅速的发展。这方面的发展，已收到最宣传的是理论的小波和他们的亲属，其中涉及扩大方面的职能，从一个单一的功能，由平移和膨胀。然而，在被称为\emph{time-frequency analysis}或\emph{Gabor analysis}的相关领域中也已经有了很大的进展，其涉及根据通过转换和调制从单个函数生成的函数集的扩展。在这一领域有一些具体和实际的问题，其研究揭示了与谐波和泛函分析方面的联系，这些方面以前被认为是相当纯粹的，也许是相当奇特的。在这篇简要的论文中，我对深奥和适用之间的一些相互作用进行了调查。它是基于我在2005年10月在阿拉哈巴德的哈里什-钱德拉研究所举行的第九次调和分析讨论会上所作的专题演讲。
英文摘要：
The area of Fourier analysis connected to signal processing theory has undergone a rapid development in the last two decades. The aspect of this development that has received the most publicity is the theory of wavelets and their relatives, which involves expansions in terms of sets of functions generated from a single function by translations and dilations. However, there has also been much progress in the related area known as \emph{time-frequency analysis} or \emph{Gabor analysis}, which involves expansions in terms of sets of functions generated from a single function by translations and modulations. In this area there are some questions of a concrete and practical nature whose study reveals connections with aspects of harmonic and functional analysis that were previously considered quite pure and perhaps rather exotic. In this expository paper, I give a survey of some of these interactions between the abstruse and the applicable. It is based on the thematic lectures which I gave at the Ninth Discussion Meeting on Harmonic Analysis at the Harish-Chandra Research Institute in Allahabad in October 2005.
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