I am getting incorrect FFT values

Hello,

The values (S) are oscillating around 50 but when i did FFT, I only got at 1.86. I don't know what is wrong with my code. Can someone help me?

%FFT 
T=0.01; %cuz the time interval is 0,01. You can see in "t"
Fs=1/T;
t=readtable('t.txt');
S=table2array(readtable('S.txt'));
L=numel(S);
%plot(t,S)
grid on 
grid minor

f=Fs*(0:(L/2))/L;
Y=fft(S-mean(S));
P2 = abs(Y/L);
P1 = P2(1:L/2+1);

Warning: Integer operands are required for colon operator when used as index.

P1(2:end-1) = 2*P1(2:end-1);
[pks,locs] = findpeaks(P1, 'MinPeakProminence' ,0.05)

pks = 0.1245

locs = 16

plot(f,P1) 
title('Amplitude Spectrums of Aggregat frequency')
xlabel('f (Hz)')
ylabel('Amplitude')
%xlim([0 150]) 
for k = 1:numel(locs)
    xline(f(locs(k)), '-r' , sprintf( 'f = %.2f' ,f(locs(k))))
end

Answer 1

[Star Strider]

The 1.86 value is correct. Look at the time domain plot —

%FFT 
T=0.01; %cuz the time interval is 0,01. You can see in "t"
Fs=1/T;
t=readtable('https://www.mathworks.com/matlabcentral/answers/uploaded_files/1287695/t.txt');
S=table2array(readtable('https://www.mathworks.com/matlabcentral/answers/uploaded_files/1287700/S.txt'));

DT = datetime(t.Var1)

DT = 805×1 datetime array
   2021-09-30 10:00:35.280
   2021-09-30 10:00:35.290
   2021-09-30 10:00:35.300
   2021-09-30 10:00:35.310
   2021-09-30 10:00:35.320
   2021-09-30 10:00:35.330
   2021-09-30 10:00:35.340
   2021-09-30 10:00:35.350
   2021-09-30 10:00:35.360
   2021-09-30 10:00:35.370
   2021-09-30 10:00:35.380
   2021-09-30 10:00:35.390
   2021-09-30 10:00:35.400
   2021-09-30 10:00:35.410
   2021-09-30 10:00:35.420
   2021-09-30 10:00:35.430
   2021-09-30 10:00:35.440
   2021-09-30 10:00:35.450
   2021-09-30 10:00:35.460
   2021-09-30 10:00:35.470
   2021-09-30 10:00:35.480
   2021-09-30 10:00:35.490
   2021-09-30 10:00:35.500
   2021-09-30 10:00:35.510
   2021-09-30 10:00:35.520
   2021-09-30 10:00:35.530
   2021-09-30 10:00:35.540
   2021-09-30 10:00:35.550
   2021-09-30 10:00:35.560
   2021-09-30 10:00:35.570

tv = second(DT) - second(DT(1));
T = mean(diff(tv))

T = 0.0100

L=numel(S)

L = 805

[pks,locs] = findpeaks(S, 'MinPeakProminence',0.10);
ApproxFreq = 1/mean(diff(tv(locs)))

ApproxFreq = 1.9886

figure
plot(tv,S)
hold on
plot(tv(locs), pks, '^r')
hold off
grid on 
grid minor

The frequency calculated from the time differences of the peaks is slightly different, however quite similar.

.

[uzzi]

Dear Star Strider, thank you very muh for your answer. This clear things up. But shouldn't the amplitude be nearly 50 since the waves are oscillating nearly 50?

[Star Strider]

As always, my pleasure!

The amplitude in the fft result is the amplitude of the oscillations. They go from about 49.85 to 50.17, for an amplitude of about 0.32. The D-C (constant) offset is about 50, and that will be present as the value at 0 Hz. The reason for subtracting the mean of ‘S’ fron ‘S’ is to prevent that value from making the peak at 1.85 Hz essentially invisible in the plot. (The amplitude of the fft result in the plot other than the 0 Hz amplitude should be multiplied by 2 to correct for the energy division between the positive and negative frequencies in a two-sided fft. That would make it about 0.28, close to the observed amplitude.)

.

[uzzi]

Ohh I see. Thank you.

[uzzi]

Hello Star strider,

Can I ask some suggestions from you? The FFT analysis can only be done with the frequency (a derived quantity) which is determined on the basis of zero crossings. But my data for frequency has no signal form like zero crossing because it is got from measurement. So, I can't perform FFT analysis with my signal.

Are there any kind of methods to do analysis with the measurement values?

[Star Strider]

You can always ask questions, and I will do my best to answer them.

The Fourier transform is based on matching the frequencies in the signal with frequencies calculated in the transform. The more closely they match, the higher the coefficient returned by the Fourier transform. (The integral transform involved in calculating the Fourier series is more complicated than that, however that will do for the purposes of this discussion.) It has nothing to do with zero-crossings, and everything to do with the oscillations in the signal, without regard to the signal base line.

The frequency approximation technique I used (deriving the frequency from the distance between the peaks, or the period of the signal), is a simple (and imprecise) calculation intended to demonstrate that the frequency estimated by the fft was essentially the same as the frequency calculated by taking the mean value of the peak periods, nothing else. It also has nothing to do with zero-crossings, although I could have done something similar to that by using the mean of the signal and then calculating the crossings of that value.

There are methods to estimate the frequency and amplitude of the various signal components that do not directly involve the Fourier transform, however they are more complicated. Most of them (that I am familiar with) involve doing a linear or non-linear regression of the signal, and estimating the parameters of that model. The Fourier transform is simpler, more efficient, and more precise.