Mean Amplitude of the signal

Hi, My problem is to calculate mean amplitude of the signal and plot it on the graph with signal course. Below you can see my source code:

      y % signal vector, where [3083 1]= size(y)
      Fs=100;
      L=length(y);
      NFFT = 2^nextpow2(L); 
      Y = fft(y,NFFT)/L;
      f = Fs/2*linspace(0,1,NFFT/2+1);

     n1=1/100; %1
     m1=L/100; %end
     [a b]=size(y);
     nov=(m1-n1)/(a-1);
     x=n1:nov:m1;

figure
subplot(2,1,1)
plot(f,2*abs(Y(1:NFFT/2+1)),color) % amplitude spectrum
subplot(2,1,2)
plot(x,y,'b') % course of the signal

Could you tell me how can I calculated mean amplitude based on this? Or maybe there exists another way to find it? When I used mean(abs(Y(1:NFFT/2+1))) and ploted it on the second subplot it was far away from signal...

Answer 1

[Wayne King]

Hi Karolina, No, it's proportional to the amplitude squared of the Fourier coefficients. You can get amplitude estimates like this:

t = 0:0.01:5-0.01;
x = cos(2*pi*4*t)+1/2*cos(2*pi*8*t)+randn(size(t));
xdft = fft(x);
xdft = (2/length(x))*xdft(1:length(x)/2+1);

Now, you have to be able to figure out that the 4-Hz component lives in DFT bin (21) and the 8-Hz component lives in DFT bin (41)

   abs(xdft(21))
   abs(xdft(41))

Give you the amplitude estimates for those frequencies.

   abs(xdft(16:51))

Gives you the amplitude estimates for 3-10 Hz.

Note that the spacing between DFT bins ist Fs/N where Fs is the sampling frequency and N is the length of the signal.

[Aqeel Syed Shamsi]

Hi Wayne, what if I want amplitude estimates for 7-13 Hz? Please reply, I shall be very thankful to you!

[Tor Aarskog]

Hi, By doing this i would get a vecor of values. Are they mean amplitudes, of the frequency range, in the time step? What would these values correspond to ?

Answer 2

[Arun Aniyan]

Hi,

I am not sure why you should do fourier transform to get the mean amplitude of your signal . For the mean amplitude of the signal for your case you can simply use

 mean_amplitude = mean(y); % Find mean amplitude

 d=ones(1,length(y)).*mean_amplitude; % A dummy vector having values of the mean
 plot(x,y); % Plot your signal
 hold all;
 plot(d);

This will give a plot with the signal , with a straight line over plotted along the signal. Or do you mean , the mean amplitude of the spectrum ?

Cheers

- Arun

[Karolina]

Hi, I would like to find average amplitude of the signal eg in the range 3 - 10 Hz?

Answer 3

[Wayne King]

Hi Karolina, You can find the average power of the signal in the [3,10] Hz band. If you have the Signal Processing Toolbox.

Fs = 100;
t = 0:0.01:1-0.01;
x = cos(2*pi*4*t)+1/2*sin(2*pi*8*t)+randn(size(t));
psdest = psd(spectrum.periodogram,x,'Fs',100,'NFFT',length(x));
pwr = avgpower(psdest,[3,10]);

You can also easily obtain what percentage of the power is contained in that interval

    pwrratio = 100*(pwr/avgpower(psdest,[0,50]));

[Karolina]

Hi Wayne, thank you very much, but is the power the same as the amplitude?