Abstract
Two different procedures for effecting a frequency analysis of a time-dependent signal locally in time are studied. 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.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">></ETX>
Keywords
Time–frequency analysisWaveletAlgorithmSIGNAL (programming language)Fourier transformWavelet transformStability (learning theory)Signal processingComputer scienceMathematicsFunction (biology)Speech recognitionArtificial intelligenceMathematical analysisComputer visionDigital signal processing
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Publication Info
- Year
- 1990
- Type
- article
- Volume
- 36
- Issue
- 5
- Pages
- 961-1005
- Citations
- 6328
- Access
- Closed
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Cite This
Ingrid Daubechies
(1990).
The wavelet transform, time-frequency localization and signal analysis.
IEEE Transactions on Information Theory
, 36
(5)
, 961-1005.
https://doi.org/10.1109/18.57199
Identifiers
- DOI
- 10.1109/18.57199