I've written a code for continuous wavelet transform using a Cauchy type wavelet function. But the intensity of wavelets aren't true. they are rippling in time. I used multiplication in the frequency space, instead of convolution in time-space. I attached a picture of results. As you can see in figure (4), the intensities of wavelets are rippling, but from figure (1) we can say that the intensities must not ripple. I'm not sure how to fix this- any suggestions?
May i suggest you either:
-use an analytic Cauchy wavelet
-perform the decomposition on the analytic signal
ie, get its Hilbert transform as an imaginary part, and then look at the absolute values of the coefficients?
If this works better, i would provide some literature and pointers to start from. If not, i will try another one, before returning to the kennel
You can also try with Q-shift type of CWT which is available in MATLAB2013
If the depicted result is obtained as the absolute value of the analytic wavelet, another problem could be the normalization factor.
When the "continuous" case is discretized the set of filters are not orthogonal. So a normalization factor must be imposed as the sum in frequency of the frequency response of each bandpass filter (i.e. each dilated wavelet).
In this situation the ripple disappear and it is possible to track the constant amplitude of each sinusoid.
If this is the case I can give you more information.
Dear Dr. Blázquez,
Thank you for the answer.
I corrected the normalization factor and it worked. So thank you very much.
This rippling could be also related to the phase jump in your signal from the higher frequency to the lower frequency. try to generate a smooth phase transition between those two components. this will reduce further the rippling.
- Badges
- Science topic
- Similar topics
- Biological Science
- Physiology
- Biosignals
- Biomedical Signal Processing