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 $f=\frac{\omega}{2\pi}=\frac{1}{2\pi s}$ (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!