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The wavelet transform is a transformation to basis functions that are localized in frequency (similar in that sense to Fourier-related transforms).As basis functions one uses wavelets.
The big advantage over the Fourier transform is the temporal (or spatial) locality of the base functions (see also short-time Fourier transform) and the smaller complexity (O(N) instead of O(N log N) for the fast Fourier transform (where N is the data size)).
In the likeness of the uncertainty principle the restriction for wavelet transform resolution can be written down:
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and this result better in times as compared to the Fourier transform
Important applications are:
Types of wavelet transforms:
- continuous wavelet transform (CWT)
- discrete wavelet transformIn numerical analysis and functional analysis, the discrete wavelet transform DWT refers to wavelet transforms for which the wavelets are discretely sampled. The first DWT was invented by Alfred Haar, a Hungarian mathematician. For an input represented by (DWT)
- fast wavelet transform (FWT)
- wavelet packets
- complex wavelet transform
1 History
- First wavelet ( Haar waveletThe Haar wavelet is the first known wavelet and was proposed in 1909 by Alfred Haar. Note that the term wavelet was coined much later. The Haar wavelet is also the simplest possible wavelet. It looks like this: | 1 O | | 1/2 0 O | | -1 | O 0 The disadvant) by Alfred Haar (1909)
- Since the 1950s: Jean Morlet and Alex Grossman
- Since the 1980s: Yves Meyer , Stephane MallatStephane G. Mallat made some fundamental contributions to wavelet theory development in the late 1980s and early 1990s. He has also done work in applied mathematics, signal processing, music synthesis and image segmentation. Specifically, he collaborated, Ingrid Daubechies , Ronald Coifman , Victor Wickerhauser
2 External links
Computer visionComputer Vision is a subfield of artificial intelligence. The purpose of computer vision is to program a computer to "understand" a scene or features in an image. Typical goals of computer vision include: The detection, segmentation, location, and recogni
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