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[Wavelet] How to convert scales to frequencies?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg119438] [Wavelet] How to convert scales to frequencies?
  • From: ZiYuan Lin <ziyuang at gmail.com>
  • Date: Fri, 3 Jun 2011 04:37:21 -0400 (EDT)
  • Reply-to: comp.soft-sys.math.mathematica at googlegroups.com

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==CF=89/(2=CF=80)=1/(2=CF=80s) (is it right?), where the discretized s' are calculated from octaves and voices, following

s_{oct,voc}==CE=B12^(oct=E2=88=921)2^(voc/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 =CE=B1=10 and  scale {4,4}=160), which is contrast to f==CF=89/(2=CF=80)=1/(2=CF=80s). I must have got some silly errors. So what is the correct frequency formula? Thank you!


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