I would like to quantify the changes in frequencies (scales to be more precise since I am using continous wavelet transformation) coefficient in time of signals composed of low frequencies 0.1-4 Hz. The signal goes from one steady state to another. Is it correct to calculate the median frequencies at each bin and see how the median frequency evolves in time? I obviously would loose some resolution since I would have to calculate my median frequency in bins that have the same size, so I have to accept the size of the biggest bin (of the lowest frequencies). It would be really helpful if somebody has a better idea or can send me some references to read. Thank you.
Lots of people do this. The basic problem, is that for estimating the spectrum you need to collect a certain number of samples in time, over a time window of width To, so you cannot have an 'instantaneous' spectrum, just a moving average of such spectral estimates. The shorter you make To, the narrower the time steps, but the frequency resolution gets poorer with small To. What people do is to overlap samples (say overlap 50% of To, or 75%, or even more), and plot the evolution of the spectrum with time. But you must be aware that the 'spectra' you plot are spectral ESTIMATES. And you need to understand its limitations of the process (such as leakage).
Wavelet transform or short time FT is a regular processing method to get result from (theoritically) any kind of signal. If you are dealing with a specific signal with some known characteristic, as you said "The signal goes from one steady state to another.", maybe you can narrow the problem down to several key parameters, such as f1 (for state 1), f2 (for state 2), and tc(for changing point) etc.
If this is possible (suitable) for your problem, you just need to optimize these parameters to fit the signal. A simple way is adjust parameters to form a signal that have least error comparing to the original signal.
hope this helps.
Thank you. I am getting so far very good results taking into consideration the limitations. I am actually calculating the moving median frequency of a lot of signals. Now I wish to average them which hopefully will give a better result.
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