Scaling a function (wavelet)

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Jakob Sørensen
Jakob Sørensen 2013-5-16
Hi there,
I got a function descriped as follows:
t = linspace(-3, 3 1024); % Time vector from -3s to 3s with 1024 points
y = (1./(1+t.^(2.^4))).*cos(20*t); % Enveloped cosine function
Now this is a wavelet, that I need to use as a mother wavelet. I now need scaled versions of it. Meaning Half duration, double frequency for each scale. Like this:
Scale: Freq: Duration:
1 20 -3.0:3.0 [s]
2 40 -1.5:1.5 [s]
3 80 -.75:.75 [s]
...etc
You probably get the point now. I tried this:
wavDur = 3/2^(m-1); % Half duration [s]
t = linspace(-wavDur, wavDur,round(2*wavDur*fs)); % Time vector
wavelet = (1./(1+t.^(2.^4))).*cos(20*t*2^(m-1)); % Scale dep. wavelet
Where m is the scale going from 1:12 atm. However this does not work. Most likely it has something to do with the envelope not scaling accordingly. Is there an easier way of scaling a signal the way I would like to? Basically its just a compression in time for each scale step.
  1 个评论
Jakob Sørensen
Jakob Sørensen 2013-5-16
Okay, as I read my own question i realized that I was quite far from the optimal method. My new code is like this
for m = scales
for n = 0:99
tScale = 2^(m-1); % Time scale factor: 2, 4, 8, 16...
tShift = 0.01*n*tScale; % Time shift factor [s]
% Calculate the scaled and shiftet wavlet
wavelet = (1./(1+(tScale*t-tShift).^4)).*cos(20*(tScale*t-tShift));
% Calculate lag zero crosscorrelaton
zeroCorr = signal*wavelet';
% Insert into coefficient matrix
coefs(m,n+1) = zeroCorr;
end
end
Scales is equal to 1:10 and n is just the time delay. Can someone tell me if this is correct? It seem to create the correct signals.

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