ContinuousWaveletData

ContinuousWaveletData[{{oct1, voc1}->coef1, ...}, wave]
yields a continuous wavelet data object with wavelet coefficients corresponding to octave and voice and wavelet wave.

Details and OptionsDetails and Options

  • ContinuousWaveletData[{{oct1, voc1}->coef1, ...}, ...] is always converted to an optimized standard form with structure ContinuousWaveletData[coefs, octvocs, ...].
  • The coefficients can be vectors, Sound[...], or SampledSoundList[...] objects.
  • The options used by ContinuousWaveletTransform can also be used as options to ContinuousWaveletData.
  • In standard output format, only the number of octaves, voices, and dimensions of the original data are printed.
  • Normal[ContinuousWaveletData[...]] gives a list of rules which gives the correspondence between each octave and voice and the corresponding coefficient array .
  • ContinuousWaveletData represents a continuous wavelet transform w(u,s)=1/(sqrt(s))sum_(k=1)^nx_k TemplateBox[{psi}, Conjugate]((Delta (k-u))/s) at multiple scales .
  • Each scale is specified by an octave number and voice number and is given by .
  • The scale can be used to extract wavelet coefficients from a ContinuousWaveletData object cwd. The following specifications can be given:
  • cwd[{oct,voc}]extract coefficients corresponding to
    cwd[{{oct1,voc1},{oct2,voc2},...}]extract several wavelet coefficient arrays
    cwd[ovpatt]extract all coefficients whose scale matches ovpatt
    cwd[All]extract all coefficients
  • By default, coefficients are returned as a list of rules .
  • can be used to control the output form. Possible include:
  • "Rules"rules
    "Values"coefficients only
    "Inverse"inverse transform individual coefficients
    "ListPlot"simple list plots for 1D coefficients
    "Sound"sound objects for sound coefficients
    "SampledSoundList"sampled sound objects for sound coefficients
  • Properties of a wavelet representation are obtained from ContinuousWaveletData[...]["prop"].
  • ContinuousWaveletData[...]["Properties"] gives a list of properties available for the ContinuousWaveletData object.
  • Properties related to transform coefficients include:
  • "Octaves"the number of octaves used
    "Voices"the number of voices per octave used
    "Scales"wavelet scales used
    "Wavelet"wavelet family used
    "WaveletScale"smallest resolvable scale
    "WaveletIndex"list of all wavelet indices
    "LogScalogramFunction"gives the function
    "LinearScalogramFunction"gives the function
  • Properties related to input data include:
  • "DataDimensions"dimensions of original data
    "DataChannels"the number of channels of data
    "DataMean"the mean of original data
    "DataWrapper"wrapper function applied to data after reconstruction
    "SampleRate"sample rate used for input data

ExamplesExamplesopen allclose all

Basic Examples (2)Basic Examples (2)

Get a ContinuousWaveletData object:

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The ContinuousWaveletData represents arrays of coefficients at different scales :

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Extract properties including numerical scale corresponding to each :

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Compute the inverse wavelet transform of arbitrary continuous wavelet transform coefficients:

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