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According to the transform $$w(u,s)=\frac{1}{\sqrt{s}}\int _{-\infty }^{\infty }x(t) \psi ^*\left(\frac{t-u}{s}\right)dt,$$ the frequency should be $f=\omega/(2\pi)=1/(2\pi s)$ (is it right?), where the discretized s' are calculated from octaves and voices, following $$s_{\text{oct},\text{voc}}=\alpha 2^{\text{oct}-1} 2^{\text{voc}/\text{nvoc}}$$ But from one second of 20Hz's humming:

WaveletScalogram[ContinuousWaveletTransform[
    Table[Sin[40 Pi x] , {x, 0, 1, 1/2048}], 
    GaborWavelet[], {6, 4}, WaveletScale -> 10]]

one can see that coefficients mainly lie in the 4th octave (in this case $\alpha=10$ and the corresponding scale {4,4}=160), which is contrast to $f=1/(2\pi s)$. I must have got some silly errors. So what is the correct frequency formula? Thank you!

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    Which wavelet are you using?2011-06-03
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    As shown in the Mathematica code, GaborWavelet2011-06-03
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    To those voting to close: this topic is too old to be migrated anymore; go easy, y'all.2013-06-17
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    @J.M. Well, it should have been in MMA.SE2013-06-17
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    Sure, but that site you speak of didn't exist at the time you asked this question (otherwise, you'd have asked it there to begin with ;) ). Anyway...2013-06-17

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