Proper wavelet scaling / restricted frequency analysis

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Dear all, I sample a signal with 20000 Hz and I'm using e.g. the morlet wavelet to analyze the frequency content of short time periods (e.g. 500 ms). Two questions: The scaling os correlated to the pseudo-freuency range of the wavelet transfrom. How can I determine the optimal scaling factor? I'm just interested in the frequency range of 100-300 Hz. Is there a possibility - e.g. through the factors - to focus the wavelet analyses on this frequency range? Looking forward to your advice. Best, Peter

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Wayne King
Wayne King 2013-5-16
编辑:Wayne King 2013-5-16
Yes, it is possible, but you have to remember that the CWT is not as localized in frequency as the Fourier basis, so you have to give yourself some wiggle room. A sine wave will not be localized at one scale in the CWT. The way to do it best depends on whether you are using cwt.m or cwtft.m.
I'll create a signal consisting of 100-Hz and 300-Hz sine waves in noise. The 100-Hz signal will occur over the first 500 msec, the 300-Hz sine wave over the interval from 500 msec to 1 second.
Here is cwt.m:
fs = 2e4;
t = 0:1/fs:2-1/fs;
x = ...
2*cos(2*pi*100*t).*(t<0.500)+3*cos(2*pi*300*t).*(t>0.500 & t <1)+randn(size(t));
dt = 1/fs;
minscale = centfrq('morl')/(300*dt);
maxscale = centfrq('morl')/(100*dt);
scales = minscale-10:maxscale+10;
cfs = cwt(x,scales,'morl','plot');
Now for cwtft (using an analytic Morlet wavelet)
MorletFourierFactor = 4*pi/(6+sqrt(2+6^2));
s0 = (0.002*MorletFourierFactor);
smax = (1/100*MorletFourierFactor);
ds =0.2;
nb = ceil(log2(smax/s0)/ds+1);
scales = struct('s0',s0,'ds',0.5,'nb',nb,'type','pow','pow',2);
cwtS1 = cwtft({x,dt},'scales',scales,'wavelet','morl');
sc = cwtS1.scales;
freq = 1./(sc*MorletFourierFactor);
contour(t,freq,abs(cwtS1.cfs));
xlabel('Time'); ylabel('Pseudo-Frequency');
  5 个评论
vinod naidu
vinod naidu 2016-5-10
编辑:vinod naidu 2016-5-10
I wanted to do in the same way for my recorded audio signal I have a [x, fs]=audioread('rec2.wav'); which loads x [81410x1] double and fs=44100
I want to scale the signal 1.65 to 2 & with the decrement of 0.005 for choosing high frequency contents ,and i want to know which one represents the a,b coefficents ? in
Akshay Ravindran
Akshay Ravindran 2017-7-2
Hi ,
Can i use the scale generated after performing cwtft as input to cwt function ( older version of cwt) .
I am a bit confused as you seem to assign linear scaling based on frequency of interest as input. How exactly does the scale factor in the older version of cwt work?

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