gives the continuous wavelet transform of a list of values xi.
gives the continuous wavelet transform using the wavelet wave.
gives the continuous wavelet transform using noct octaves with nvoc voices per octave.
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.
Examplesopen allclose all
Basic Examples (2)
Basic Uses (6)
Use Normal to get all wavelet coefficients explicitly:
Also use All as an argument to get all coefficients:
WaveletScalogram gives a time scale representation of wavelet coefficients:
Time and Scale Features (4)
Use GaborWavelet to perform a continuous wavelet transform:
Verify using a WaveletScalogram:
Wavelet Families (6)
Padding has no effect on the length of wavelet coefficients:
Padding pads the input data to the next higher power of 2 to reduce boundary effects:
WaveletScale indicates the smallest resolvable scale used for the transform:
Identify Features (2)
Filter Frequencies (2)
ContinuousWaveletTransform can be used to filter frequencies:
Perform InverseContinuousWaveletTransform on a thresholded data object:
Possible Issues (1)
Based on the length of input data, the Automatic setting for octaves resolved 8 octaves:
Neat Examples (1)
Scalogram of a Zeta function:
Wolfram Research (2010), ContinuousWaveletTransform, Wolfram Language function, https://reference.wolfram.com/language/ref/ContinuousWaveletTransform.html.
Wolfram Language. 2010. "ContinuousWaveletTransform." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/ContinuousWaveletTransform.html.
Wolfram Language. (2010). ContinuousWaveletTransform. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/ContinuousWaveletTransform.html