MATLAB: Two times fft of the signal

fft

Ouput of the first fft is a sinc function. Now i need to convert the frequency axis of first fft into time domain. After that I need to take fft again and get a rectangular waveform. I have doubt that when i map the frequeny axes of the first fft into time axes at that time, the amplitude of fft remains in the frequency domain only. I am just changing the axes from frequency to time. So when i take the second fft so indirectly i am taking the fft two times of the original signal? And result shoud be rectangular waveform?

Best Answer

Yes. It's a property of the Fourier Transformation: the FT of a box is a sinc, and the FT of a sinc is a box. So if you compute fft(fft(box)) you end up with a box function.

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MATLAB: Do I get a high frequency oscillation when I take the FFT of a rectangular pulse

The results you are getting from the FFT are correct and expected. The reason for the oscillations is because the Rectangular Pulse is not centered about zero, which results in a phase shift of the FFT output. The phase shift is essentially negating every other element (odd samples) of the output of the FFT which causes the high frequency oscillation you're observing. This is explained by the time-shifted Fourier Transform Theorem.

One way to avoid the oscillations is to use FFTSHIFT on the Rectangular Pulse before taking the FFT. For example if "rect" is the Rectangular Pulse:

fftrect=fftshift(fft(fftshift(rect)));

Best Answer

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