function [xCD, kstart] = splitstepfourier(x, D, lambda, z, Tsamp,gamma,stepnum)
  %% Simulate chromatic dispersion.
  %% Params:
  %%  - x: input waveform (pulse-shaped)
  %%  - D: dispersion coefficient (ps / (nm km))
  %%  - lambda: wavelength (nm)
  %%  - z: length of fibre (km)
  %%  - Tsamp: sampling time (s)
  %% Output:
  %%  - xCD: x after being dispersed. Energy of xCD is not normalized.
  %%  - kstart: starting index of the discrete signal

  %% Convert everything to SI base units
  c = 299792458; % m/s
  D = D * 1e-6; % s/m^2
  lambda = lambda * 1e-9; % m
  z = z * 1e3; % m

  gamma = gamma * 1e-3; % watt^-1 / m
  %stepnum = 1
  dz = z / stepnum;

  hhz = 1j * gamma * dz;


  %% Time domain filter length, needed for compatibility with
  %% time-domain (convolution) chromatic dispersion.
  kmax = floor(abs(D) * lambda^2 * z / (2 * c * Tsamp^2));
  kstart = 1 - kmax;

  x = [zeros(kmax, 1); x]; % prepend zeros to allow for transients

  xCD = x .* exp(abs(x) .^ 2 .* hhz / 2);
  for i = 1 : stepnum
    xDFT = fft(xCD);
    n = length(xCD);
    fs = 1 / Tsamp;

    omega = (2*pi * fs / n * [(0 : floor((n-1)/2)), (-ceil((n-1)/2) : -1)]).';
    dispDFT = xDFT .* exp(-1j * omega.^2 * D * lambda^2 * dz / (4 * pi * c));

    xCD = ifft(dispDFT);

    xCD = xCD .* exp(abs(xCD) .^ 2 .* hhz / 2);
  end
  xCD = xCD .* exp(-abs(xCD) .^ 2 .* hhz / 2);

  if ceil(kmax/2) > 0
    %% fix the order of the samples due to prepending zeros before FFT
    xCD = [xCD(ceil(kmax/2):end); xCD(1:ceil(kmax/2)-1)];
  end
  %% pad zeros for compatibility with time-domain filter
  xCD = [zeros(floor((kmax-1)/2), 1); xCD; zeros(ceil((kmax+1)/2), 1)];
end
%% References
%% [1]: S.J. Savory, Digital filters for coherent optical receivers, 2008.