Math @ Duke

Publications [#287090] of Ingrid Daubechies
Papers Published
 Daubechies, I, The wavelet transform, timefrequency localization and signal analysis
(January, 2009),
pp. 442486
(last updated on 2018/10/17)
Abstract: © 2006 by Princeton University Press. All Rights Reserved. Two different procedures are studied by which a rrequency analysis of a timedependenl signal can be effected, locally in lime. The lirst procedure is the shorttime 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 timefrequency density. Finally the notion of "timefrequency localization" is made precise, within this framework, by two localization theorems.


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