I'd like to ask a theoretical question about power spectra.
In MATLAB, by means of a particular approach, I'm trying to generate a Gaussian variable which embodies a particular power spectrum.
The theoretical power spectrum has been calculated over an illimited range (
[-Inf,Inf]), whereas the simulated one is obtained only in a short wave number vector range.
Generally, theoretical power spectrum and simulated one look like in the figure below
green plots represent the simulated spectrum for two different configuration; the
blue line stays for the theoretical spectrum.
I'd like to know if there is any easy way to recover the spectrum loss in the high frequency region, in order to force the simulated spectrum perfectly match the theoretical. I was thinking of a fairly easy filter working this way
filter = sqrt(S_th.^2./S_sim.^2); S_rec = filter.*S_sim;
Do you believe such a procedure is allowed and physically reasonable?