# ContinuousWaveletTransform

ContinuousWaveletTransform[{x1,x2,}]

gives the continuous wavelet transform of a list of values xi.

ContinuousWaveletTransform[data,wave]

gives the continuous wavelet transform using the wavelet wave.

ContinuousWaveletTransform[data,wave,{noct,nvoc}]

gives the continuous wavelet transform using noct octaves with nvoc voices per octave.

ContinuousWaveletTransform[sound,]

gives the continuous wavelet transform of sampled sound.

# Details and Options  • ContinuousWaveletTransform gives a ContinuousWaveletData object.
• Properties of the ContinuousWaveletData cwd can be found using cwd["prop"]. A list of available properties can found using cwd["Properties"].
• The resulting wavelet coefficients are arrays of the same dimensions as the input data.
• The possible wavelets wave include:
•  MorletWavelet[…] Morlet cosine times Gaussian GaborWavelet[…] complex Morlet wavelet DGaussianWavelet[…] derivative of Gaussian MexicanHatWavelet[…] second derivative of Gaussian PaulWavelet[…] Paul wavelet
• The default wave is .
• The default value for noct is given by , where is the length of the input.  »
• The default value for nvoc is 4.
• The continuous wavelet transform of a function is given by .
• The continuous wavelet transform of a uniformly sampled sequence is given by .
• The scaling parameter is given by equal-tempered scale where is the octave number, the voice number, and the smallest wavelet scale.
• For each scale , the ContinuousWaveletTransform computes the wavelet coefficients .
• The following options can be given:
•  Padding None how to extend data beyond boundaries SampleRate Automatic samples per unit WaveletScale Automatic smallest resolvable scale WorkingPrecision MachinePrecision precision to use in internal computations
• Padding pads the input data to the next higher power of 2 to reduce boundary effects. The settings for Padding are the same as for the padding argument used in ArrayPad.
• InverseContinuousWaveletTransform gives the inverse transform.

# Examples

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## Basic Examples(2)

Compute a continuous wavelet transform using MexicanHatWavelet:

 In:= Out= Plot the coefficients:

 In:= Out= Perform an inverse continuous wavelet transform:

 In:= Out= Transform a sampled Sound object:

 In:= In:= Out= Plot a scalogram:

 In:= Out= ## Neat Examples(1)

Introduced in 2010
(8.0)