IFFT outputs complex; Input has no Nan, no Inf, & taking it from full FFT spectrum

Hi all,

I've read through & applied solutions/suggestions from other posts, yet to no avail.

I am trying to reconstruct what is happening in this paper: Acceleration, Velocity, and Displacement Spectra

Basically, they give you the signal for acceleration, then they FFT it for the spectra, then do A(f)./(2*pi*i*f) or A(f)./((2*pi*i*f)^2) to get the velocity/displacement spectra, respectively.

I am good up to this point, then they state we can now get the time series signal by IFFT'ing the acc, vel, disp respective spectrums.

I IFFT'd the two sided spectrum of the acceleration, and plotted it against the original signal; it was a success, they overlap perfectly.

My issue is with taking the IFFT of the velocity and displacement spectra. I keep getting complex doubles as the output.

What i've done:

• I realized that while I did this --> A(f)./(2*pi*i*f) or A(f)./((2*pi*i*f)^2) to obtain the velocity/displacement spectrums, A(f) was the one sided spectrum of acceleration; I needed the two sided spectrum of acceleration when performing the IFFT for vel/displ. This resulted in better looking complex doubles that were not all Inf in the real part (unlike when I used the one sided).
• I followed the link here to fix obtaining the frequency array size to correctly represent a two sided spectrum derivative of function using discrete fourier transform matlab

• I found that if you have any Nan or +/-Inf as an input to an IFFT, it can mess up the entire thing, & sure enough, I had them at index 1 and 1001. Just to troubleshoot, I took these out and just concatenated what I wanted like [v_dfft(2:1001) v_dfft(1002:2000)]

After doing all this, the IFFT still shows up as a complex double. I am unfortunately unaware on how to check for even or odd symmetry in the real and imaginary parts. I am also rusty on choosing perfect N or the time vector, but from trial and error (not the preferred method, obviously) I got my FFT spectrums to match, so I think those are OK.

I would really like to be able to learn how to do this, as it could help my research in wave energy a lot.

Thanks & let me know if you'd like to see anything else. I can include the code, it's just long-ish

• Chris