WaveletScale

WaveletScale

is an option for ContinuousWaveletTransform and related constructs used to specify the smallest resolvable scale.

Details

  • WaveletScale represents the smallest resolvable scale in a ContinuousWaveletTransform.
  • The continuous wavelet transform of a uniformly sampled sequence is given by w(u,s)=1/(sqrt(s))sum_(k=1)^nx_k TemplateBox[{psi}, Conjugate]((Delta (k-u))/s).
  • The scaling parameter is given by equal-tempered scale where is the octave number, the voice number, and the smallest wavelet scale.
  • The default value for WaveletScale is Automatic. The value of can be any number greater than 0.

Examples

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Basic Examples  (1)

WaveletScale indicates the smallest resolvable scale used for the transform:

The scales used are given as with wavelet scale, octave, and voice:

Properties & Relations  (1)

Automatic value of WaveletScale is computed as the inverse of Fourier wavelet length of the wavelet:

MorletWavelet[]:

GaborWavelet[w]:

DGaussianWavelet[n]:

MexicanHatWavelet[σ]:

PaulWavelet[n]:

Wolfram Research (2010), WaveletScale, Wolfram Language function, https://reference.wolfram.com/language/ref/WaveletScale.html.

Text

Wolfram Research (2010), WaveletScale, Wolfram Language function, https://reference.wolfram.com/language/ref/WaveletScale.html.

CMS

Wolfram Language. 2010. "WaveletScale." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/WaveletScale.html.

APA

Wolfram Language. (2010). WaveletScale. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/WaveletScale.html

BibTeX

@misc{reference.wolfram_2025_waveletscale, author="Wolfram Research", title="{WaveletScale}", year="2010", howpublished="\url{https://reference.wolfram.com/language/ref/WaveletScale.html}", note=[Accessed: 21-February-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_waveletscale, organization={Wolfram Research}, title={WaveletScale}, year={2010}, url={https://reference.wolfram.com/language/ref/WaveletScale.html}, note=[Accessed: 21-February-2025 ]}