
FFT2DX.OMS
Script File:
# Description:
# Computes a two dimensional Fourier transform.
#
clear
# total time, g(t1, t2) is "small" for (t1, t2) > T / 2
T = 4.
# number of data points, dt resolves time integrals
N = 16
# time between data values
dt = T / N
# time between frequency values
df = 1 / T
# time grid
t = (seq(N)  N / 2  1) * dt
# exponent in definition of h(t)
alpha = 5.
# h(t) = exp(  alpha * t)
h = exp(  alpha * abs(t))
# g(t1, t2) = h(t1) * h(t2)
g = fillcols(h, N) % fillrows(h', N)
#
# Plot g near the origin.
gtitle("g(t1, t2)")
surface(g)
gupdate
#
# the continuous transform of g(t1, t2) is given by
# G(f1, f2) = H(f1) * H(f2)
# where H(f) = 2 * alpha / ((2 * PI * f)^2 + alpha^2)
# is the discrete transform of g
G = real(fft2d(complex(g))) * dt * dt
gaddwin
gtitle("G(f1, f2)")
surface(G)
Output:

