spectrogram understanding amplitude and normalised frequency

Hi experts

I am trying to understand how the amplitude and frequency is expressed with the 'spectrogram' command in matlab. I have the following code:

Fs = 500;
t = 0:1/Fs:10-1/Fs;                   

 x1 = 10*cos(2*pi*50*t);
 x2 = cos(2*pi*60*t  + 45*(pi/180));
 x3 = cos(2*pi*70*t+ 10*(pi/180));

 x = x1+x2+x3;


[s,f,t]=spectrogram(x)
 
 am = abs(s);
 tol = 280;
 s(abs(s) < tol) = 0;
 ph = angle(s);
 
 figure
 subplot(2,1,1)
 plot(f,am(:,1))
 subplot(2,1,2)
 plot(f,ph(:,1)*(180/pi))

S gives me a complex matrix wich i can calculate the amplitude and phase with abs(S) and angle(S). When i plot the spectrum in amplitude-frequency domain for a certain time i get the following:

• First of all i have 3 components on 50Hz, 60Hz and 70Hz. I alreay looked up what normalized frequency means and if im right the normalised frequency is /calculated as: f/fNyquist. So with a sample frequency of 500Hz the nyquist freq is 250Hz. Shouldnt this give 50/250=0.2, 60/250=0.24 and 70/250=0.28 as normalised frequency? instead i get 0.62, 0.75 and 0.88. What could be the problem here?
• My second question is how the amplitude is expressed? For x1 = 10*cos(2*pi*50*t); i get an amplitude of 2970 and for x2 = cos(2*pi*60*t + 45*(pi/180)); i get an amplitude of 295. What does this exactly mean? an amplitude of 1 in time domain corresponds with 300... in frequency domain.
• phase plot fft (strange)values here my problem with the phase was fixed but now i see a similar problem wich i dont quite know how to fix. When i use a normal fft i get the phases that i want.

Kind regards

[hosein Javan]

if you are measuring a power signal, I say instead of using spectrogram, use fft. spectrogram uses window function. if you can estime your signal frequency, you can cut a piece of your signal and perform an fft analysis. it's very simple though.