Wavelet transform, time-frequency localization and signal analysis
Summary form only given, as follows. Two different procedures are studied by which a frequency analysis of a time-dependent signal can be effected, locally in time. 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.
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