The wavelet transform, time-frequency localization and signal analysis

作者：Ingrid Daubechies · 发表于：IEEE Transactions on Information Theory · 年份：1990 · DOI：10.1109/18.57199 · 被引用次数：6496 · 研究领域：Image and Signal Denoising Methods、Blind Source Separation Techniques、Machine Fault Diagnosis Techniques

Two different procedures for effecting a frequency analysis of a time-dependent signal locally in time are studied. The first procedure is the short-time or windowed Fourier transform; the second is the wavelet transform, in which high-frequency components are studied with sharper time resolution than low-frequency components. The similarities and the differences between these two methods are discussed. For both schemes a detailed study is made of the reconstruction method and its stability as a function of the chosen time-frequency density. Finally, the notion of time-frequency localization is made precise, within this framework, by two localization theorems.>