dft

dft.py

# Example usage
# $ python dft.py | gnuplot
# 9
# 0 0
# 1 1
# 2 2
# 0 2
# 1 1
# -1 1
# 0 2
# -2 2
# -1 1

import math

N = int(raw_input())

f = []
for i in range(N):
    (x, y) = map(float, raw_input().split())
    f.append(complex(x, y))

F = []
for i in range(N):
    ang = -2 * 1j * math.pi * i / N
    r = 0
    for j in range(N):
        r += (math.e ** (ang * j)) * f[j]
    F.append(r)

print "set parametric"
print "set samples", N + 1

print "x(t)=",
for i in range(N):
    ang = 2 * math.pi * i / N
    if i > 0:
        print "+",
    print F[i].real / N, "*cos(", ang, "*t)-",
    print F[i].imag / N, "*sin(", ang, "*t)",

print
print "y(t)=",
for i in range(N):
    ang = 2 * math.pi * i / N
    if i > 0:
        print "+",
    print F[i].imag / N, "*cos(", ang, "*t)+",
    print F[i].real / N, "*sin(", ang, "*t)",

print
print "plot [t=0:", N, "] x(t), y(t)"
print "pause 60"

I try to plot the graph in Desmos, but it gives out a lot of circles...
The equation is the one on your blog.

Seems if samples are too high, the graph will be in chaos, like the projection of the curve in the complex space to the plane.