Math @ Duke

Publications [#287134] of Ingrid Daubechies
Papers Published
 Daubechies, I, Wavelet transform, timefrequency localization and signal analysis,
IEEE Transactions on Information Theory, vol. 36 no. 5
(1990),
pp. 9611005 [doi]
(last updated on 2018/07/22)
Abstract: Two different procedures for effecting a frequency analysis of a timedependent signal locally in time are studied. The first procedure is the shorttime or windowed Fourier transform; the second is the wavelet transform, in which highfrequency components are studied with sharper time resolution than lowfrequency 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 timefrequency density. Finally, the notion of timefrequency localization is made precise, within this framework, by two localization theorems.


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