# Description:
# Inverse discrete Fourier transform of a sinc function
#
clear
# number of points in the transform
N = 256 
# number of points where h(t) = 1
M = 32 
# half the rectangular window width
T = .5 
# time between points
dt = 2 * T / M 
# spacing between frequency points
df = 1. / (N * dt) 
# frequency grid
f = (seq(N) - N / 2 - 1) * df 
# so we do not divide by zero
f(N / 2 + 1) = 1e-4 * T 
# the sinc function
H = sin(2 * pi * T * f) / (pi * f) 
#
# compute the approximate continuous inverse transform
h = ifft(complex(H)) * df
#
# plot the result
t = (seq(N) - N / 2 - 1) * dt
gxaxis("linear", - 1, + 1, 4, 5)
gxtitle("Time")
gtitle("Inverse Fourier Transform")
gplot(t, real(h))