W = output Wigner distribution
Ex = Input electric field (MUST be a column vector
Notes:
W = Int(-inf..inf){E(x+y)E(x-y)exp[2ixy]}
E(x+y) & E(x-y) are calculated via a FFT (fast Fourier transform) using the
shift theorem. The integration is performed via a FFT. Thus it is important for the data to satisfy the sampling theorem:
dy = 2*pi/X X = span of all x-values dy = y resolution
dx = 2*pi/Y Y = span of all y-values dx = x resolution
The data must be completely contained within the range x(0)..x(N-1) & y(0)..y(N-1) (i.e. the function must fall to zero within this range).
your delay is always half of the signal
the matrix can be too large
for chirp test the max locations should be at phase 2*f*b*t but the max is alwayes at the center
You have to think what you are doing - given data of length N, the Wigner distribution is N^2, so clearly with N=10^5, N^2 = 10^10 - you're not going to ever be able to make such a Wigner distribution.
However, it is possible that you do not need the Wigner distribution over the whole temporal and spectral domains. Unfortunately I have not implemented this yet.