wavelet

A wavelet is a wave-like oscillation with an amplitude that begins at zero, increases or decreases, and then returns to zero one or more times. Wavelets are termed a "brief oscillation". A taxonomy of wavelets has been established, based on the number and direction of its pulses. Wavelets are imbued with specific properties that make them useful for signal processing. thumb|Seismic wavelet

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Image: Meyer wavelet.svg

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Commons category: Wavelets
Commons gallery: Wavelet

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~31 min read

Article

29 sections

Contents

Etymology
Wavelet theory
Continuous wavelet transforms (continuous shift and scale parameters)
Discrete wavelet transforms (discrete shift and scale parameters, continuous in time)
Multiresolution based discrete wavelet transforms (continuous in time)
Time-causal wavelets
Mother wavelet
Comparisons with Fourier transform (continuous-time)
Definition of a wavelet
Scaling filter
Scaling function
Wavelet function
History
Timeline
Wavelet transforms
Generalized transforms
Applications
As a representation of a signal
Wavelet denoising
Multiscale climate network
List of wavelets
Discrete wavelets
Continuous wavelets
Real-valued
Complex-valued
See also
References
Further reading
External links

For example, a wavelet could be created to have a frequency of middle C and a short duration of roughly one tenth of a second. If this wavelet were to be convolved with a signal created from the recording of a melody, then the resulting signal would be useful for determining when the middle C note appeared in the song. Mathematically, a wavelet correlates with a signal if a portion of the signal is similar. Correlation is at the core of many practical wavelet applications.