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in the cartoon below enter image description here

It shows that if we take the inverse Fourier transform of a Hermitian function, real part even and imaginary part is odd we should get a purely real function in the time domain.

I tried to replicate this by taking a frequency response I have, zero padding it making it even for the real and odd in the imaginary. Shown below enter image description here Although my ifft in Matlab I still have a significant imaginary component, the real is shown left and imaginary on the right. enter image description here I also wrote my own script for DFT/IDFT and tested it on a sine function to make sure I get the same as Matlab. Maybe I have missed something?

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  • $\begingroup$ Are you using the whole input vector, or are you specifying an fft length when calling fft? Also, a simple one-sample shift will lead to a sinusoidal modulation after dft; make sure you're using the right ,fftshift`ifftshift` $\endgroup$
    – Marcus Müller
    Aug 18, 2016 at 11:32
  • $\begingroup$ Maybe it's a numerical/rounding issue? Note that your imaginary part is 1/100th scale of the real part. $\endgroup$
    – Atul Ingle
    Aug 18, 2016 at 15:02
  • $\begingroup$ I solved my issue, I had to be very careful in replicating the signal, i wrote it all on paper so i could visually see everything... Should I close the question $\endgroup$
    – JS60
    Aug 22, 2016 at 10:29

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A (near) sinusoid in one domain (zoom in off center, and you might see it) can indicate a shift away from symmetry in the other domain. So your initial imaginary signal may be 1 or 1/2 samples off from exact circular symmetry around element 0 (maybe around element 1 in MatLab or Fortran weird array indexing)

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  • $\begingroup$ Yeh thanks, I had to be extra careful, I really do not like how matlab index starts from 1 :( $\endgroup$
    – JS60
    Aug 22, 2016 at 10:30

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