The wavelet transform, time-frequency localization and signal analysis
1990/01/01 by Ingrid Daubechies, I. Daubechies · 6,471 citations
Computer Science · Engineering · Mathematics · #Algorithm #Artificial intelligence #Blind Source Separation Techniques #Computer science #Computer vision #Digital signal processing #Fourier transform #Function (biology) #Image and Signal Denoising Methods #Machine Fault Diagnosis Techniques #Mathematical analysis #Mathematics #SIGNAL (programming language) #Signal processing #Speech recognition #Stability (learning theory) #Time–frequency analysis #Wavelet #Wavelet transform
paper · doi:10.1109/18.57199
published in IEEE Transactions on Information Theory 36(5), 961-1005 (Institute of Electrical and Electronics Engineers)
openalex publication_date 1990/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.>
Citations
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