yields a continuous wavelet data object with wavelet coefficients coefi corresponding to octave and voice {octi,voci} and wavelet wave.

Details and Options

  • ContinuousWaveletData[{{oct1,voc1}->coef1,},] is always converted to an optimized standard form with structure ContinuousWaveletData[coefs,octvocs,].
  • The coefficients coefi 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 {{oct1,voc1}->coef1,{oct2,voc2}->coef2,} which gives the correspondence between each octave and voice {octi,voci} and the corresponding coefficient array coefi.
  • 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 {oct,voc} 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 {oct,voc}
    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 {{oct1,voc1}->coef1,{oct2,voc2}->coef2,}.
  • cwd[,{form1,form2,}] can be used to control the output form. Possible formi include:
  • "Rules"rules {{oct1,voc1}->}
    "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 {octi,voci}
    "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


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Basic Examples  (2)

Get a ContinuousWaveletData object:

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The ContinuousWaveletData represents arrays of coefficients at different scales {oct,voc}:

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Extract properties including numerical scale corresponding to each {oct,voc}:

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

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Scope  (12)

Options  (5)

Properties & Relations  (5)

See Also

ContinuousWaveletTransform  InverseContinuousWaveletTransform  WaveletScalogram  DiscreteWaveletData

Introduced in 2010