BUILT-IN MATHEMATICA SYMBOL
ContinuousWaveletData
ContinuousWaveletData[{{oct1, voc1}->coef1, ...}, wave]
yields a continuous wavelet data object with wavelet coefficients 
corresponding to octave and voice 
and wavelet wave.
- 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
)/s)](Files/ContinuousWaveletData.en/7.png "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 |
Get a ContinuousWaveletData object:
| Out[1]= |  |
The ContinuousWaveletData represents arrays of coefficients at different scales 
:
| Out[2]= |  |
Extract properties including numerical scale corresponding to each 
:
| Out[3]= |  |
Compute the inverse wavelet transform of arbitrary continuous wavelet transform coefficients:
| Out[1]= |  |
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