wny fft does't work with different signal?

I am using fft to extract freq content in my two type of time series. First, time series (file sig_fft.txt) look good and showing some speaktral peak. but unfortunately for second time series (event.txt) no single spectral appear. I even using IFFT as checking wheater fft result can get back the original signal. For me seems FFT is work well. But I still wonder why my FFT having strange result on second one. Can anyone explain why ? Or do I make something wrong in my coding?

Second thing, I wonder about the amplitude on freq domain, does it shoul be the same in the time domain? I read several literature taht it relates to power which is square of amplitude, but why some coding that i found abot fft using 2*abs(fft_result)?

please help this beginner to get more about fft

here modification the code and time series that I use

%PERFORM FFT of data TO GET FREQ CONTENT
data=load("event.txt");
n=length(data(:,1));
srate=1000; %sampling rate 
nyq=srate/2;
dataX=fft(data(:,2))/n;
hz=linspace(0,nyq,floor(n/2)+1);
figure (1) 
subplot(211)
plot(data(:,1),data(:,2))
xlabel('Time(sec)'), ylabel('Amplitude')
subplot(212)
plot(hz,2*abs(dataX(1:length(hz))),'-r'), xlabel('Freq(Hz)')
%set(gca,'XLim',[0 2],'YLim',[0 100])

%Perform IFFT TO CONSTRUCT ORIGINAL SIGNAL
recon_data=ifft(dataX)*n;
figure(2)
subplot(211)
plot(data(:,1),data(:,2)), xlabel('Time(sec)')
legend('original data')
title('inverse fourier transform')
subplot(212)
plot(data(:,1),real(recon_data),'-r')
legend('reconstruction data')

Answer 1

[Star Strider]

Thbere is a farily significant D-C or constant offset in ‘data(:,2)’ and that hides all the spectral peaks of lower magnitudes.

The eassiest way to avoid this is to subtract the D-C offset value (that is actually the mean value of the signal) before calculating the fft:

dataX=fft(data(:,2)-mean(data(:,2)))/n;

that I did here. The spectral peak at about 225 Hz becomes visible. There is nothing wrong with your code (that I can see).

‘Second thing, I wonder about the amplitude on freq domain, does it shoul be the same in the time domain?’

It will be close, however the energy in the signal is distributed over a wide spectrum, so it will rarely be exactly the same. There is also the problem that the fft may not calculate a frequency at exactly the frequency of a particular signal component, so that energy may be spread over a short range of adjacent frequuencies.

Try this —

%PERFORM FFT of data TO GET FREQ CONTENT
data=load("event.txt");
n=length(data(:,1));
srate=1000; %sampling rate 
nyq=srate/2;
dataX=fft(data(:,2)-mean(data(:,2)))/n;
hz=linspace(0,nyq,floor(n/2)+1);
figure (1) 
subplot(211)
plot(data(:,1),data(:,2))
xlabel('Time(sec)'), ylabel('Amplitude')
subplot(212)
plot(hz,2*abs(dataX(1:length(hz))),'-r'), xlabel('Freq(Hz)')

%set(gca,'XLim',[0 2],'YLim',[0 100])

%Perform IFFT TO CONSTRUCT ORIGINAL SIGNAL
recon_data=ifft(dataX)*n;
figure(2)
subplot(211)
plot(data(:,1),data(:,2)), xlabel('Time(sec)')
legend('original data')
title('inverse fourier transform')
subplot(212)
plot(data(:,1),real(recon_data),'-r')
legend('reconstruction data')

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