BUILT-IN MATHEMATICA SYMBOL

# ContinuousWaveletTransform

ContinuousWaveletTransform[{x1, x2, ...}]
gives the continuous wavelet transform of a list of values .

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 OptionsDetails 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.

## ExamplesExamplesopen allclose all

### Basic Examples (2)Basic Examples (2)

Compute a continuous wavelet transform using MexicanHatWavelet:

 Out[1]=

Plot the coefficients:

 Out[2]=

Perform an inverse continuous wavelet transform:

 Out[3]=

Transform a sampled Sound object:

 Out[1]=
 Out[2]=

Plot a scalogram:

 Out[3]=