MATLAB: How to see what child wavelets is ‘cwt’ using

Question

The function 'cwt' takes as arguments a mother wavelet as well as a scaling vector.

How can I see the resulting child wavelets that are internally used to calculate the coefficients of the transformation?

Answer 1

The 'cwt' of a function with the analyzing wavelet can be written as the convolution of the signal with the conjugate and time reverse of the wavelet (at each scale). Therefore, you can use a delta function as the function to be analysed. The conjugate and time reverse of the wavelet coefficients at each scale will then *approximate *the wavelet at that scale. Please find an example below:

a0 = 2^(1/32);
scales = a0.^(4*32:8*32);
% Shifted delta function
x = zeros(1024,1);
x(512) = 1;
cfs = cwt(x,scales,'cmor1-1.5',1);
cfs = flip(conj(cfs),2);
subplot(211)
plot([real(cfs(10,:))' imag(cfs(10,:)')])
grid on;
xlim([1 1024])
legend('real part','imaginary part');
subplot(212)
plot([real(cfs(100,:))' imag(cfs(100,:)')])
grid on;
xlim([1 1024])
legend('real part','imaginary part');