cwt (Wavelet Toolbox)

cwt	Examples See Also

Continuous 1-D wavelet coefficients.

Syntax

coefs = cwt(s,scales,'wname')
coefs = cwt(s,scales,'wname','plot')

Description

cwt is a one-dimensional wavelet analysis function.

coefs = cwt(s,scales,'wname') computes the continuous wavelet coefficients of the vector s at real, positive scales, using the wavelet whose name is 'wname' (see waveinfo).

coefs = cwt(s,scales,'wname','plot') computes, and in addition plots, the continuous wavelet transform coefficients.

Let s be the signal and

the wavelet. Then the wavelet coefficient of s at scale a and position b is defined by:

since s(t) is a discrete signal, we use a piecewise constant interpolation of the s(k) values, k = 1 to length(s).

Then for any strictly positive scale a, we compute C_a,b for b = 1 to length(s).

Output argument coefs contains the wavelet coefficients for the scales within the vector scales in the same order, stored rowwise.

Examples of valid uses are:

c = cwt(s,1:32,'meyr')
c = cwt(s,[64 32 16:-2:2],'morl')
c = cwt(s,[3 18 12.9 7 1.5],'db2')

Examples

This example demonstrates the difference between discrete and continuous wavelet transforms.

% Load original fractal signal. 
    load vonkoch 
    vonkoch=vonkoch(1:510); 
    lv = length(vonkoch);

    subplot(311), plot(vonkoch);title('Analyzed signal.'); 
    set(gca,'Xlim',[0 510])

% Perform discrete wavelet transform at level 5 by sym2. 
% Levels 1 to 5 correspond to scales 2, 4, 8, 16 and 32. 
    [c,l] = wavedec(vonkoch,5,'sym2');

% Expand discrete wavelet coefficients for plot. 
% Levels 1 to 5 correspond to scales 2, 4, 8, 16 and 32. 
    cfd = zeros(5,lv); 
    for k = 1:5 
        d = detcoef(c,l,k); 
        d = d(ones(1,2^k),:); 
        cfd(k,:) = wkeep(d(:)',lv); 
    end 
    cfd = cfd(:); 
    I = find(abs(cfd)<sqrt(eps)); 
    cfd(I)=zeros(size(I)); 
    cfd = reshape(cfd,5,lv);

% Plot discrete coefficients. 
    subplot(312), colormap(pink(64)); 
    img = image(flipud(wcodemat(cfd,64,'row'))); 
    set(get(img,'parent'),'YtickLabels',[]); 
    title('Discrete Transform, absolute coefficients.') 
    ylabel('level')

% Perform continuous wavelet transform by sym2 at all integer 
% scales from 1 to 32. 
    subplot(313)
    ccfs = cwt(vonkoch,1:32,'sym2','plot'); 
    title('Continuous Transform, absolute coefficients.') 
    colormap(pink(64)); 
    ylabel('Scale')

Algorithm

since s(t) = s(k), if

then

so at any scale a, the wavelet coefficients C_a,b for b = 1 to length(s) can be obtained by convolving the signal s and a dilated and translated version of the

integrals of the form

(given by intwave), and taking finite difference

using diff.