Fast Fourier Transform from data in file

Hello everyone,

I am getting vector length error in a matlab code. The problem is that I don't know how to construct vectors properly.

The file contains single column of electric field time domain data. Number of rows are 19838, which means the time of recording is sampled at these points. Total time is around 33 picoseconds.

Now I want to convert this time domain data to frequency domain data in range 0.001 to 6 GHz. How should I sample my frequency?

My code:-

load Ez_time.txt
file = Ez_time;
aa = fft(file);

 %File contains 19838 rows each correspoing to 
% one time step. Total time is around 33 picoseconds.
T =length(file);   
Fs = 1/T;

 %For taking fft in a frequency range 0.001 to 6 GHz
freq = 0.001 : 1./T : 6;
plot(freq,abs(aa));

Alternatively, I also tried below written code, but this isn't giving me the right spectrum.

 load Ez_time.txt
file = Ez_time;
aa = fft(file);

 freq = linspace(0,6,19838);
plot(freq,abs(aa))

Answer 1

[Star Strider]

Try this:

L = length(file);                                       % Signal Length
t = linspace(0, 1, L)*33E-12;                           % Time Vector (s)
Ts = mean(diff(t));                                     % Sampling Time (s)
Fs = 1/Ts;                                              % Sampling Frequency (Hz)
Fn = Fs/2;                                              % Nyquist Frequency (Hz)
aa = fft(file)/L;                                       % Fourier Transform (Scaled)
Fv = linspace(0, 1, fix(L/2)+1)*Fn;                     % Frequency Vector (One-Sided)
Iv = 1:length(Fv);                                      % Index Vector

figure(1)
plot(Fv, abs(aa(Iv))*2)
set(gca, 'XLim',[0.001 6]*1E+9)

The plot is not going to be very informative, since the steps of the frequency vector are 30.3015 GHz. You will have to sample at a much higher frequency if you want any detail in that range.

[Jitendra Kumar Singh]

Thanks for answering. However there are few glitches. Doesn't the sampling frequency become too high. I calculated the value of Fs, it gave me 6e14. But then I divided Fs by 1e8 to get a sampling frequency of 6e6 and multiplied Fv by 1e3 to get points from 0 to 3e9. But sadly, the spectrum is not even close.

[Star Strider]

My pleasure.

The sampling interval, and from it the sampling frequency, are calculated correctly from the data you provided. (You can easily check them.)

Assuming regular sampling, the sampling interval, ‘Ts’, is 33E-12/L, or 1.6635 femtoseconds. The sampling frequency is the reciprocal of that, 601 THz.

The rest of my code is derived from this documentation for the fft (link) function.

[Jitendra Kumar Singh]

Thank you very very much. Your code worked when I made the steps smaller(0.003 GHz). You have ended my painful journey of 2 days of finding fft.

Thanks a ton!!!!!

[Star Strider]

As always, my pleasure!

Answer 2

[miki90]

Hello. I didn't want to start the different topic for the same problem, so I will be thankful if anyone can help me. I have the data in the file, gained from the acquisition in LabVIEW. There is a matrix of voltages in the file, with frequency sampling of 1kHz, and the number of samples - 10000. I need to find the frequency range in which the signal belongs to, using these data. I tried to follow the example found on the Mathworks site, but I get only the straight horizontal line with the one peak at about 2.5, which is the magnitude. Can anyone help me with this task? Thanks in advance.

[Jitendra Kumar Singh]

Hey, I didn't had any course on signal processing. But some how I figured out how to take FFT. If you give some details about your data like total time for which the data is acquired, expected frequencies in the data etc, I might be able to help you.

[Star Strider]

@miki90 — I find this documentation on the fft (link) function a bit easier to follow.