From frequency to time domain

I have the function S, representing the sea elevation spectrum in frequency domain.

S= 300x365 , being the spectra for 365 days in 300 frequency timestep.

I want to translate the function to time domain, simulating S for every second in a day (86400s).

How can I implement this?

thank you in advance.

Answer 1

[Jon]

If I understand what you are asking for correctly I am assuming that your matrix S has the fft of the original time domain data.

I think you could then recover it and interpolate to get data for every second in the day using:

% make time vector for original spacing (300 samples per day)
t = linspace(0,86400-1,300);
% recover time domain signal
X = ifft(S);
% interpolate intermediate values
tq = 0:86400-1;
Xq = interp1(t,X,tq)

[Jon]

Alternatively, to do the interpolation, I think you could insert zeros appropriately into the spectrum and then do the ifft, but I'd have to think about the details of how that is done.

[Nicolò Monaco]

Thank you for your answer. My problem was that the spectrum is not directly derived by an fft but you provide me a feasible solution.

[Jon]

Glad that you were able to make progress