# Mathematica: How to convert scales to frequencies?

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? –  endolith Jun 3 '11 at 12:06
As shown in the Mathematica code, GaborWavelet –  ziyuang Jun 3 '11 at 14:46
To those voting to close: this topic is too old to be migrated anymore; go easy, y'all. –  J. M. is back. Jun 17 '13 at 14:43
@Ｊ.M. Well, it should have been in MMA.SE –  ziyuang Jun 17 '13 at 16:05
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... –  J. M. is back. Jun 17 '13 at 16:08