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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http://bit.ly/5mQWBT Exploring the world of #cetacean and #avian acoustics using #wavelets
thisisnonplus (Bobby Wilks |Nonplus) Sun, 13 Dec 2009 08:47:49 -0000
http://bit.ly/5mQWBT Exploring the world of #cetacean and #avian acoustics using #wavelets
Wavelets, Approximation, and Statistical Applications (Lecture Notes in Statistics) http://tinyurl.com/yd22wp7 #Ebook
agungabb (agungabb) Sun, 13 Dec 2009 05:23:53 -0000
Wavelets, Approximation, and Statistical Applications (Lecture Notes in Statistics) http://tinyurl.com/yd22wp7 #Ebook
Whale song art: dolphin calls turned into kaleidoscopic patterns using wavelets http://ow.ly/LcOv (via @brainpicker) Awesome!
MarkTrueblood (Mark Trueblood) Sun, 13 Dec 2009 01:03:25 -0000
Whale song art: dolphin calls turned into kaleidoscopic patterns using wavelets http://ow.ly/LcOv (via @brainpicker) Awesome!
Running into patterns &mosaics everywhere today! via @brainpicker Dolphin calls -> wavelets -> kaleidoscopic patterns http://ow.ly/LcOv #Art
sanjeevn (sanjeev ) Sat, 12 Dec 2009 21:19:24 -0000
Running into patterns &mosaics everywhere today! via @brainpicker Dolphin calls -> wavelets -> kaleidoscopic patterns http://ow.ly/LcOv #Art
Fun with math // Whale song art: dolphin calls turned into kaleidoscopic patterns using wavelets http://ow.ly/LcOv (via @brainpicker)
strangeglow (John Worthington) Sat, 12 Dec 2009 21:05:24 -0000
Fun with math // Whale song art: dolphin calls turned into kaleidoscopic patterns using wavelets http://ow.ly/LcOv (via @brainpicker)
Whale song art: dolphin calls turned into kaleidoscopic patterns using wavelets http://ow.ly/LcOv
brainpicker (Maria Popova) Sat, 12 Dec 2009 20:20:38 -0000
Whale song art: dolphin calls turned into kaleidoscopic patterns using wavelets http://ow.ly/LcOv

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