In mathematics, wavelets, wavelet analysis, and the wavelet transform refers to the representation of a signal in terms of a finite length or fast decaying oscillating waveform (known as the mother wavelet). This waveform is scaled and translated to match the input signal. In formal terms, this representation is a wavelet series, which is the coordinate representation of a square integrablefunction with respect to a complete, orthonormal set of basis functions for the Hilbert space of square integrable functions. Note that the wavelets in the JPEG2000 standard are biorthogonal wavelets, that is, the coordinates in the wavelet series are computed with a different, dual set of basis functions.
Overview
The word wavelet is due to Morlet and Grossman in the early 1980s. They used the French word ondelette - meaning "small wave". A little later it was transformed into English by translating "onde" into "wave" - giving wavelet. Wavelet transforms are broadly classified into the discrete wavelet transform (DWT) and the continuous wavelet transform (CWT). The principal difference between the two is the continuous transform operates over every possible scale and translation whereas the discrete uses a specific subset of all scale and translation values.
Using wavelet theory
Wavelet theory is applicable to several other subjects. All wavelet transforms may be considered to be forms of time-frequency representation and are, therefore, related to the subject of harmonic analysis. Almost all practically useful discrete wavelet transforms make use of filterbanks containing finite impulse response filters. The wavelets forming a CWT are subject to Heisenberg's uncertainty principle and, equivalently, discrete wavelet bases may be considered in the context of other forms of the uncertainty principle.
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Bibliographies on Wavelets - Bibliographies on wavelets at the University of Karlsruhe.
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Discovering Wavelets - A center of activity for incorporating wavelets into the undergraduate curriculum. Tutorials, projects and resources.
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The Bath Wavelet Warehouse - A collection of wavelet filters available for download.
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The Wavelet Digest - Bringing together the Wavelet Community. This site hosts a free monthly newsletter on wavelets. Covers theory and applications. Contains all archives since it was founded in 1992 by Wim Sweldens.
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Wavelet Forum - A friendly posting board on wavelets.
Splines and orthogonal wavelets: Daubechies construction View the complete course at: http://ocw.mit.edu/18-085F07 ...