标准时频变换探讨

Discussion on normal time-frequency transform

为了整合Gabor变换、小波变换和S变换,本文给出标准时频变换(NTFT)的简单定义和典型表达形式,并介绍了标准窗的概念;指出标准Gabor变换和标准小波变换是NTFT的2类特殊表现形式。NTFT的主要功能是时频分析、时频滤波和信号预测,指明这3种功能的数学基础,其中着重介绍了从信号的NTFT中直接提取(或估计)简谐或准简谐项的无为方法;并论述了广义S变换与NTFT的异同。

In order to integrate Gabor transform, wavelet transform and S transform, this paper gave a simple definition of normal time-frequency transform （NTFT） and showed a classical expression of the NTFT, in which the concept of normal window was introduced. It was indicated that normal Gabor transform and normal wavelet transform are two special forms of the NTFT. Three kinds of NTFT applications： time-frequency analysis, time-frequency filtering and signal prediction were showed with their mathematical bases. Particularly, a method, named as ＂Inaction＂, to estimate or extract the harmonic or quasi-harmonic terms directly from the NTFT of a signal was introduced. Moreover, the difference between generalized S- transform and NTFT was discussed.