I wantadvice on a practical issue that we are facing while trying to get the high t-f resolution for hopping signals recorded through voice communication.
There are multiple signals occurring at the same time with a large dynamic range. The Wigner Ville distribution is applied but the main drawback of this distribution is the cross terms. Other variations like Pseudo Smooth WV was also tried but the results were not satisfactory. Moreover, when there are two frequencies, one of high power than the other, occurring at the same time, the frequency of the higher power is more dominant in the resulted PS WV distribution.
Choi William distribution gives better clarity of TF distribution for multiple signals but the boundary where the hoping frequency changes is not clearly detected.
It would be good if someone could suggest or guide me through the selection of methods including or excluding time-frequency distributions that give high clarity so that the hop rate and frequency can be detected via spectrum.
convolve the wigner distribution with the one dimensional kernl i.e smooth it along time axis. All the cross-terms will be parallel to time axis therefore ID smoothing will be enough. Try to convole WD with number of 1D filters of varying length and then combine them by choosing a minimum value at each t-f point.
Other option could be to use spectrogram of different window lenghts and combine them by choosing a minimum value at each t-f point. You can see my paper entitled 'Improved resolution short time fourier transform".
@Nabeel and Zhao: I have tried all these techniques but the problem persist. You are right if we do these operation offline. Issue which I may have missed is the online or real time nature of the speech signals as multiple streams are continuously being received.
Power spectrum of the signal? The FWHM of the 0 peak should give you a measure of the hops (assuming that is the lowest frequency in the signal).
As I anderstand your signal is composed of several frequencies. This model is called multicomponent signal. Thus maybe the parametric time-frequency algorithm can help you. I.e. using Lee-Morf algorithm you can estimate not only frequencies of multi-component signal but also the moment of changes of the parameters of the model. So try the parametric t-f transform.
If the technique that I proposed is working offline then it can be extended to online by appending zeros to the signal before computing its t-f representation.
Imran, when at the university, I had to measure the average dimension of supergranulation of Sun surface.
So, we are talking about images, but in the end that's data, aren't they?
Anyhow, granulation looks like bright discs on the Sun surface separated by dark boundaries, but it is actually the top of pillars of hot material rising from lower layers in Sun atmosphere.
And the exercise is simply to compute the autocorrelation (the antitransform of the power spectrum) of a region of interest.
You can find more details on this pdf (in Italian, sorry):
http://personal.ifae.es/maiorino/Docs/MOF.pdf
Oooops, sorry! I checked the link, and I can find no more the document there (I changed my job since I used that server).
But I found the original document (written in WordPerfect back then) and it says: to find the average dimensions of a structure through autocorrelation it suffices to find the FWHM of the peak in the origin.
I believe you can make a simple gaussian fit of the zero peak (a few samples in the autocorrelation signal, put it in log scale, fit to a quadratic), and thence recover the peak FWHM. That should be a measure of your hop.
I hope this fits your needs.
Thanks Marino, Nabeel, Zhao and Boguslaw. Now things are better with ur advices.
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