fft/ifft: Sampling Frequency and Length of Signal
fft, ifft, matlab, signal-processing
Solution
When you use the abs(fft()) in ifft, you are using only the amplitude of the signal and dropping the phase information, which is needed.
Use the whole signal (removed abs):
plot(real(ifft(fft(x)))); % fft then ifft
Problem
This is partly taken from the Matlab fft-documentation: ``` Fs = 30; % Sampling frequency T = 1/Fs; % Sample time L = 130; % Length of signal t = (0:L-1)*T; % Time vector x = sin(2*pi*1*t); % 1 Hz sinus plot(real(ifft(abs(fft(x))))); % fft then ifft % Fs = 30, L = 60 / 90 / 120 ... : ok % Fs = 20, L = 60 / 80 / 100 ... : ok % Fs = 30, L = 50 / 70 / 80 ... : not ok ``` It seems to me that whenever the length of the signal is a multiple of the sampling frequency, the sinusoid is reconstructed correctly (apart from some shift), e.g. here `Fs = 30, L = 60`: However, if for example `Fs = 30, L = 80` (not a multiple), the result looks odd: Is this behaviour correct? Why is this happening and how can I avoid this? Just throw away some part of the signal such that the length "fits" the sampling frequency?