Q: Difference between summation of motion components and IFFT? I want to use IFFT to obtain the time signal from freqency data, being response amplitude operators (RAO's) and phase shifts of a vessel over frequency range 0.1-2.6 RAd/s, having 200 samples. I first used a very unrefined method to obtain the time domain response as follows:
for i=1:length(t)
    surgedisp(:,i)=surge_amp(:,1).*cos(g(:,i)+surge_phase(:,1)+phase(:,1));
    surge(1,i)=sum(surgedisp(:,i));
end

Here, g represents w*t, surge phase is the phase shift of the surge motion wrt the waves, phase is a random phase (multiple of 2pi) of the random (ocean)wave. (The values at each frequency)
For the use of IFFT, I needed to represent the surge_amplitudes and surge_phases into the complex form in order to use IFFT:
Z=surge_amp.*exp(j*surge_phase+j*phase), followed by IFFT(Z), and obtain the time signal.
I think I get totally wrong results and I don't know in which direction to look for. Can it have something to do with the j*wt part that I should incorporate into Z? And can someone tell me if the first method is equivalent to the IFFT method?
