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 MexicanHatWavelet[].
- 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
open allclose allBasic Examples (2)
Compute a continuous wavelet transform using MexicanHatWavelet:
Perform an inverse continuous wavelet transform:
Transform a sampled Sound object:
Scope (18)
Options (9)
Applications (4)
Properties & Relations (1)
Possible Issues (1)
Neat Examples (1)
See Also
InverseWaveletTransform ContinuousWaveletData DiscreteWaveletTransform WaveletScalogram WaveletMapIndexed
Related Guides
Introduced in 2010
(8.0)