Dear Sir,

Quite fundamentally, if you want to resolve both frequency and time at the same time, you are 'trapped' by the Heisenberg uncertainty principle of Quantum Mechanics, which basically tells you this is impossible.

More in detail, if you observe a certain signal for a time duration T, you are only able to resolve its frequency up to a certain delta-f = 1/T. (There may be a small scale factor missing here. It could also be delta-f = 1/2T)

Given this limitation, as far as I am concerned, I think in general resolving time and frequency of a signal is very often done in audio compression codecs, like MP3. (there are a whole lot others too.) These codecs usually divide the signal in time windows, then take the DCT (discrete cosine transform) in each window. On top, some of these codecs have adaptive window length control, meaning they detect signals with sharp attack times, and then reduce the window length. This of course results in reduced frequency resolution for the signal, as, per Heisenbergs principle, you cannot resolve time and frequency at the same time.

Best Regards,

Henri.

you can use the periodogram of matlab 

You can use the Wigner-Ville transform, or Wavelets transform.

Dear Raghu

These answers are correct and just to add that the octave-band Discrete

Wavelet Transform (DWT) and the more flexible Wavelet Packet Transform (WPT)  are improvements over the normal short term Fourier Transform which uses a fixed window, unlike the WT. I attach a paper I gave years ago (1998?), on applying these WT's to EEG (brain signals) for separating mental tasks,  which might help you.

Regards

Paul

Thanks for valuable information to all

It might be easiest to resolve the frequency component  up to an extent using f = 1/T.

Frequency component at each instant of time have no meaning. Frequency component make sense only for a given duration of waveform. If you see the equation of Fourier transform/series then you may notice that for each frequency component the whole waveform in time domain is required. You may use DFT tools available in many simulators (being a circuit designer I use SPICE waveform viewer). The lowest frequency component is limited by the time duration (1/T) and highest by the number of points taken to calculate the frequency spectrum.