use of fft, ifft and fftshift in matlab -
i trying implement split-step fourier method solve nonlinear schrodinger equation in optics. treats linear part , nonlinear part separately. solves linear part using fourier transform , nonlinear part in time domain.
the following code copied book:
alpha = 0 beta_2 = 1 gamma = 1 t = linspace(-5,5,2^13); delta_t = t(2)-t(1); l = max(size(a)); delta_omega = 1/l/delta_t*2*pi; omega = (-l/2:1:l/2-1)*delta_omega; = 2*sech(t); a_t = a; step_num = 1000; h = 0.5*pi/step_num; results = zeros(l,step_num); a_f = fftshift(fft(a_t)); n=1:step_num a_f = a_f.*exp(-alpha*(h/2)-1i*beta_2/2*omega.^2*(h/2)); a_t = ifft(a_f); a_t = a_t.*exp(1i*gamma*(abs(a_t).^2*h)); a_f = fft(a_t); a_f = a_f.*exp(-alpha*(h/2)-1i*beta_2/2*omega.^2*(h/2)); a_t = ifft(a_f); results(:,n) = abs(a_t); end where a_t pulse (the function solved). don't understand in beginning uses fftshift shift 0 frequency center, later in loop doesn't have fftshift. tried adding fftshift main loop, or removing in beginning. both give wrong results, why that? in general, when should use fftshift , ifftshift, when trying solve differential equation in case?
thanks
seems like, trying simulate soliton propagation sech laser. can partially clarify doubt plotting signals images , noticing apparent difference, did when tried same.
firstly, use fftshift , ifftshift or not depends on type of signal working on.
fft function considers signal begin @ 0 , unlike cases use in signal processing. same ifft.
your actual negative side considered inverted , shifted extreme right, making actual plot example -5 5 0 10.
that's use fftshift rearrange data centered @ 0.
if want shift signal unordered form compute fft or ifft (which should), should use ifftshift. not shifting ifft. opposite of fftshift.
ok, make things simple follow switch case-
switch (signal): {
case(signal has both -ve , +ve parts, centered @ zero):
- apply ifftshift make unordered before fft or ifft
- apply fftshift result output same signal form. causal signal.
case( signal unordered ):
- directly apply fft or ifft.
- apply fftshift result if want see in causal type.
case( applying both fft , ifft simultaneously ):
- go on, alright. worry signal when performing single operations
}
i've worked on same year back. if there necessary additions or corrections made in answer, feel free put in comments.
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