Need to Decrease the Width of FFT

Hi

I'm quite new to MATLAB. I'm working on spectral analysis of a signal and trying to obtain its FFT. But the problem is that my spectral lines are coming out to be quite braod and eventually, data analysis is not possible. I'm using the following code for the obtaining the FFT:

M = 2.5e-4; Fs = 1/M; T = 1/Fs; L=1000000; NFFT = 2^nextpow2(L); Y = fft(ias, NFFT)/L; f = Fs/2*linspace(0,1,NFFT/2+1); plot(f,2*abs(Y(1:NFFT/2+1)))

Kindly suggest some solution for this problem.

Thanks and Regards.

Answer 1

[Rick Rosson]

Please try the following code. To increase the resolution of the Fourier spectrum, increase the value of the parameter k (and vice versa):

% Up-Sampling factor:
k = 4;

[M,N] = size(ias);       

% Zero pad the signal:
ias = [ias ; zeros((k-1)*M,N) ];
M = k*M;

% Time domain:
dt = 2.5e-4;
t = dt*(0:M-1)';

% Frequency domain:
Fs = 1/dt;
dF = Fs/M;
f = (-Fs/2:dF:Fs/2-dF)';

% Discrete Fourier Transform:
Y = fftshift(fft(ias))/M;

% Plot the spectrum:
figure;
plot(f,abs(Y));

HTH.

[Chirag]

Thanks a lot for the answer.

I tried the code. But it didn't work. There is no change in the width. I varied the value of M from 4 to 4000.

I think the problem is with the data points. Is there anyway I can increase the number of data points in my code. For the sake of simplicity, I'm taking the FFT of a sin wave with freq of 50 HZ, but the spectral line is from 48.5 to 51.5 Hz. It might be due to less number of data points being fed to FFT function.

Thanks a lot again.

[Chirag]

I think if i'm able to increase the data points, problem will be solved. Please let me know if there is any way to do so.

Thanks.

Answer 2

[Christos Saragiotis]

Dear Chirag,

From what you say, I understand that you want to decrease the df of your spectrum. You know that df = 1/(N dt), where N is the number of your samples and dt = 1/fs is the sampling interval. Therefore, df = 1/T where T = N dt is the total time of observation.

So in order to make df finer, you need to increase the time of recording, T.

When you just zero-pad (as when you take the 2^nextpow2), your figure will have a finer df but in fact the resolution hasn't increased. fft just "interpolates" the values.

Regards,

Christos

[Rick Rosson]

Yes, that is correct.

[Chirag]

Thank you for your reply. I tried the method you suggested, but unfortunately it didn't work.

Kindly, go through the link to have a better look at my problem:

https://docs.google.com/leaf?id=0B4dPcFFHHl9VZGM3ZmJiMWItYzAyMy00YjAxLWFhOWUtYTA3YjRiNTI3ODE4&hl=en_US

Thanks and regards.

Answer 3

[Rick Rosson]

Hi Chirag,

If you know that the input signal is a pure-tone sine wave at 50 Hz, then you can simply generate the signal to any length that you want. The more samples you add to the sine wave, the narrower will be the resulting spectral line.

Please try the following:

   % Up-Sampling factor:
   k = 4;

   [M,N] = size(ias);       
   M = k*M;

   % Time domain:
   dt = 2.5e-4;
   t = dt*(0:M-1)';

     % Generate pure tone sine wave:

     A = 1;
     Fc = 50;

     ias = A*cos(2*pi*Fc*t);

   % Frequency domain:
   Fs = 1/dt;
   dF = Fs/M;
   f = (-Fs/2:dF:Fs/2-dF)';

   % Discrete Fourier Transform:
   Y = fftshift(fft(ias))/M;

   % Plot the spectrum:
   figure;
   plot(f,abs(Y));

HTH.

Rick

[Chirag]

Thank you for your reply. I tried the method you suggested, but unfortunately it didn't work.

Kindly, go through the link to have a better look at my problem:

https://docs.google.com/leaf?id=0B4dPcFFHHl9VZGM3ZmJiMWItYzAyMy00YjAxLWFhOWUtYTA3YjRiNTI3ODE4&hl=en_US

Thanks and regards.