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 integrable function 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

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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

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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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@rfarrjr you guys using crucible? It's pretty sweet... and the idea of wavelets would be awesome as well. Do you use Bamboo for builds?
mattssmith (Matthew Smith) Wed, 04 Nov 2009 18:11:51 -0000
@rfarrjr you guys using crucible? It's pretty sweet... and the idea of wavelets would be awesome as well. Do you use Bamboo for builds?
Comments on #crucible code reviews should be #wavelets. That would be bad-ass :) (via @estebistec)
rfarrjr (Robert Farr) Wed, 04 Nov 2009 17:09:41 -0000
Comments on #crucible code reviews should be #wavelets. That would be bad-ass :) (via @estebistec)
Comments on #crucible code reviews should be #wavelets. That would be bad-ass :)
estebistec (Steven Cummings) Wed, 04 Nov 2009 16:40:48 -0000
Comments on #crucible code reviews should be #wavelets. That would be bad-ass :)
Anyone using Google Wave will want to get the add-on for Firefox to notify you of new waves and wavelets http://is.gd/4N2EA #googlewave
kinboshi (Daniel Phillips) Wed, 04 Nov 2009 15:58:02 -0000
Anyone using Google Wave will want to get the add-on for Firefox to notify you of new waves and wavelets http://is.gd/4N2EA #googlewave
En modo no colaborativo, las waves son blocs de notas multimedia y la manera de fusionar wavelets es todavia user-unfriendly.
martacho (Miguel R. Artacho) Wed, 04 Nov 2009 15:45:14 -0000
En modo no colaborativo, las waves son blocs de notas multimedia y la manera de fusionar wavelets es todavia user-unfriendly.
les waves s'emballent à trois éditeurs synchro dans les wavelets ;)
sophiemaheo (Sophie Maheo) Tue, 03 Nov 2009 23:24:35 -0000
les waves s'emballent à trois éditeurs synchro dans les wavelets ;)

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