Scaling a function (wavelet)

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.

[Jakob Sørensen]

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.