The wavelet transform, time-frequency localization and signal analysis
Two different procedures are studied by which a rrequency analysis of a time-dependenl signal can be effected, locally in lime. The lirst procedure is the short-time or windowed Fourier transform, the second is the "wavelet transform," in which high frequency components are sludied wilh sharper time resolution than low frequency components. The similarities and the differences between these two methods are discussed. For both scbemes a detailed study is made of Ibe reconslruetion method and ils 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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