| 1 | function [xCD, kstart] = chromaticDispersion_FFT(x, D, lambda, z, Tsamp) |
| 2 | %% Simulate chromatic dispersion. |
| 3 | %% Params: |
| 4 | %% - x: input waveform (pulse-shaped) |
| 5 | %% - D: dispersion coefficient (ps / (nm km)) |
| 6 | %% - lambda: wavelength (nm) |
| 7 | %% - z: length of fibre (km) |
| 8 | %% - Tsamp: sampling time (s) |
| 9 | %% Output: |
| 10 | %% - xCD: x after being dispersed. Energy of xCD is not normalized. |
| 11 | %% - kstart: starting index of the discrete signal |
| 12 | |
| 13 | %% Convert everything to SI base units |
| 14 | c = 299792458; % m/s |
| 15 | D = D * 1e-6; % s/m^2 |
| 16 | lambda = lambda * 1e-9; % m |
| 17 | z = z * 1e3; % m |
| 18 | |
| 19 | %% Time domain filter length, needed for compatibility with |
| 20 | %% time-domain (convolution) chromatic dispersion. |
| 21 | kmax = floor(abs(D) * lambda^2 * z / (2 * c * Tsamp^2)); |
| 22 | kstart = 1 - kmax; |
| 23 | |
| 24 | x = [zeros(kmax, 1); x]; % prepend zeros to allow for transients |
| 25 | |
| 26 | xDFT = fft(x); |
| 27 | n = length(x); |
| 28 | fs = 1 / Tsamp; |
| 29 | |
| 30 | omega = (2*pi * fs / n * [(0 : floor((n-1)/2)), (-ceil((n-1)/2) : -1)]).'; |
| 31 | dispDFT = xDFT .* exp(-1j * omega.^2 * D * lambda^2 * z / (4 * pi * c)); |
| 32 | |
| 33 | xCD = ifft(dispDFT); |
| 34 | |
| 35 | if ceil(kmax/2) > 0 |
| 36 | %% fix the order of the samples due to prepending zeros before FFT |
| 37 | xCD = [xCD(ceil(kmax/2):end); xCD(1:ceil(kmax/2)-1)]; |
| 38 | end |
| 39 | %% pad zeros for compatibility with time-domain filter |
| 40 | xCD = [zeros(floor((kmax-1)/2), 1); xCD; zeros(ceil((kmax+1)/2), 1)]; |
| 41 | end |
| 42 | %% References |
| 43 | %% [1]: S.J. Savory, Digital filters for coherent optical receivers, 2008. |