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AWT

Analytical Wavelet Transform

Calling Sequence

awt = AWT(x,nvoice,Name,sigma2,par2);

Parameters

Inputs:

x :

signal, could be complex

nvoice:

number of voices default = 12

Name :

Type of Window function, so far only "Gaussian" window available

sigma2 :

first parameter, for Gaussian window, it could be variance, default = 1

par2 :

another parameter, for Gaussian, it's xi(shifting frequency) default = 5

Outputs:

awt :

Analytical wavelet transform of x

Description

Coarsest scale is '2', finest scale is (log2(n)-5); awt is a n by nscale matrix;

Examples

n = 1024;
t = ((1:n)./n - .5).*%pi;
f = exp(%i*t.^2);
awt = AWT(f);
ImageCWT(awt,'Individual','hot');
ix = [((n/2+1):n),(1:n/2)];
plot(abs(awt(ix,1)))    // should looks Gaussian
plot(abs(awt(ix,13)))    // should looks Gaussian
plot(abs(awt(ix,25)))    // should looks Gaussian

See also

Bibliography

Mallat, "A Wavelet Tour of Signal Processing";

4.4.3 Analytical Wavelet Transform

Authors

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