Math @ Duke

Publications [#287134] of Ingrid Daubechies
Papers Published
 Daubechies, I, The Wavelet Transform, TimeFrequency Localization and Signal Analysis,
Ieee Transactions on Information Theory, vol. 36 no. 5
(January, 1990),
pp. 9611005, Institute of Electrical and Electronics Engineers (IEEE) [doi]
(last updated on 2019/09/23)
Abstract: Two different procedures are studied by which a frequency analysis of a timedependent signal can be effected, locally in time. The first procedure is the shorttime 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 timefrequency density. Finally the notion of “timefrequency localization” is made precise, within this framework, by two localization theorems. © 1990 IEEE


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