After an FFT of a signal is done, it is plotted as in the image below, with the original signal is on the first subplot.
Using the magnitude and phase data of each frequency, it's reconstructed, and the produced signal is as the image below.
The reconstructed is signal is good except it's shifted 4 milliseconds earlier from the the original signal. I also has done this with another signal, but this 4 milliseconds shift is there too. Why does this happen?
Additional question: I used this for harmonic analysis of 50 Hz fundamental frequency (electric power system frequency). I had a slightly hard time determining which frequency of each harmonic (50*n Hz) frequency to use because, from the FFT result, the phase angle is θ at (50*n∓0.001) Hz but suddenly becomes θ±180° at (50*n±0.001) Hz. For example, at 149.999Hz the phase angle is 223.3° but at 150.001Hz the phase angle is suddenly 403.3°. Is this hard time determining which angle of each frequency to use for reconstruction, normal?
By the way, this is the Matlab code I use to do the FFT and the plotting.
Fs = 1/(8e-6); % Sampling frequency
T = 1/Fs; % Sample time
L = 2^21; % Length of signal
t = (0:L-1)*T; % Time vector
SampleNoBallast; % The original signal
NFFT = 2^nextpow2(L); % Next power of 2 from length of y
Y = fft(y,NFFT)/L; % The Fast Fourier Transform producing FFT complex
f = Fs/2*linspace(0,1,NFFT/2+1); % Frequencies to plot
P = rad2deg(unwrap(angle(Y))); % Phase degrees from FFT complex
% Plotting the original signal
subplot(3,1,1); plot(t(1:12500),y(1:12500))
title('Arus Masukan LED T8 Opple 18 W tanpa Ballast')
ylabel('arus (mA)')
xlabel('waktu (s)')
grid on
set(gca,'ButtonDownFcn','selectmoveresize');
% Plot single-sided amplitude spectrum.
% Plotting the magnitude of each frequency
subplot(3,1,2); plot(f(1:17000),2*abs(Y(1:17000)))
title('Hasil FFT')
xlabel('Frekuensi (Hz)')
ylabel('Amplitudo (mA)')
set(gca,'ButtonDownFcn','selectmoveresize');
% Plotting the phase of each frequency
subplot(3,1,3); plot(f(1:17000),P(1:17000))
title('Sudut Komponen Harmonik')
xlabel('Frekuensi (Hz)')
ylabel('Sudut (derajat)')
set(gca,'ButtonDownFcn','selectmoveresize');
ifftthen there is something very wrong. If you're doing some modification of the original FFT data or using something other thanifftto reconstruct it, then we need to see that to be able to answer your question. $\endgroup$ – Peter K.♦ Mar 18 '16 at 18:53