Spectrum analyzers work based on fast fourier transform phenomena.there are two parameters that determine the interval in which you can perform a fourier transform correctly. the fist is the sampling frequency and the second is the number of sampled  points defined for transform algorithm. according to Nyquist theorem, the sampling frequency should be two times the highest frequency component in the spectrum. Hence, for shortening the interval you should increase the sampling frequency in order to prevent aliasing errors. on the other hand you should capture low frequency components by increasing the number of points or else, you will lose them.

Dear Fernando,

I believe you can do this using MATLAB. I can explain through an example. Let's first set up some parametrs:

Fs = 1000;          % Sampling frequency

T = 1/Fs;             % Sampling period

L = 1500;             % Length of signal

t = (0:L-1)*T;        % Time vector

Next, let's form a signal containing a 50 Hz sinusoid of amplitude 0.7 and a 120 Hz sinusoid of amplitude 1.

S = 0.7*sin(2*pi*50*t) + sin(2*pi*120*t);

Then, compute the Fourier transform of the signal.

Y = fft(S);

Compute the two-sided spectrum P2 and form the single-sided spectrum P1 using P2 and the even-valued signal length L.

P2 = abs(Y/L);

P1 = P2(1:L/2+1);

P1(2:end-1) = 2*P1(2:end-1);

Define the frequency domain f and plot the single-sided amplitude spectrum P1.

f = Fs*(0:(L/2))/L;

plot(f,P1)

You would observe the amplitude of the component at 50 Hz. as 0.7. Similarly, the amplitude of the component at 120 Hz. would appear as 1.

In your application, the observed signal S would be formed by the successive short time intervals of the analyzed biomedical signal.

Best of luck,

Dear Fernando,

The Composite modulation (AM-FM) is a type of modulation that covers the advantages of both modulation types. It has a lot of details you need to knew, please see the paper: under the title -

Performance improvement of SSB-FM Sub optimum demodulates

Good Luck.

Prof. S. EL-Rabaie

 Dear Prof. S. EL-Rabaie,

Thank you very much for your answer. According to your suggestion, I found the link below, but the paper there does not answer my question. How can I efficiently determine the amplitude of an AM-FM signal in short time intervals? Besides, which window function is the best option? I've used STFT with L-size Hanning window functions, and 50% overlap. Do you recommend another better option?

Thank you, and thank you Profs. Olcay AKAY and Hamid Reza Moazami!

Fernando

Article Performance Improvement of SSB-FM Suboptimum Demodulators

Dear Fernando,

STFT could be a good choice for analyzing nonstationary signals whose frequency content changes with respect to time. For example, a chirp signal (linear FM) is one of the simplest type of nonstationary signals. STFT is calculated via the command spectrogram in MATLAB. In spectrogram, the ampliltudes of the signal components are represented by different colors corresponding to varying intensity levels. The length of the analysis window is important. Because, if you choose a short length window, this gives better time resolution (time localization) but bad frequency resolution (blurring of frequency). If you use longer windows, that provides better frequency resolution, but bad time resolution (time vs. frequency trade-off). Since you are looking for frequency estimates, for your application it would be wiser to use a longer window. In my opinion, this is more critical than the type of the window (Hamming, Kaiser, boxcar etc.).

On the other hand, STFT is only one of a family of tools called time-frequency representations (TFRs). Wigner-Ville distribution, Choi-Williams distribution etc. are some other TFRs. You can try them out as well. Luckily, there is a time-frequency toolbox of MATLAB. You can check out the following web page:

http://tftb.nongnu.org/refguide.pdf    

Have a nice study,

Thank you so much Prof. Olcay AKAY. Since I need to process on realtime, I found the attached paper that seems to fit my needs. Since it is useful for noise-free sinudoids, I have to assess its performance for noisy sinudoids.

Best regards,

Fernando

http://iopscience.iop.org/article/10.1088/1748-0221/7/04/P04001

You can use some wavelet tranform.