npointDFT

npointdft.py

#! /usr/bin/python
# -*- coding: utf-8 -*-
# N点DFT行列のtexソースを吐く

import sys
import fractions

def reduce(p, q):
	common = fractions.gcd(p, q)
	return (p // common, q // common)

def dftOutput(n):
	print "\\begin{equation*}\n\\begin{pmatrix}"
	for i in xrange(n):
		print "X(\\omega _{" + str(i) + "}) \\\\"
	print "\\end{pmatrix}\n=\n\\begin{pmatrix}"
	for i in xrange(n):
		for j in xrange(n):
			if j != 0:
				sys.stdout.write(" &")
			if i == 0 or j == 0:
				sys.stdout.write("1")
			else:
				tmp = reduce(2*i*j, n)
				if tmp[0] == 1:
					frac = ("\\pi", str(tmp[1]))
				else:
					frac = (str(tmp[0]) + "\\pi", str(tmp[1]))
				if frac[1] == "1":
					sys.stdout.write("e^{-j" + frac[0] + "}")
				else:
					sys.stdout.write("e^{-j\\frac{" + frac[0] + "}{" + frac[1] + "}}")
		print " \\\\"
	print "\\end{pmatrix}\\begin{pmatrix}"
	for i in xrange(n):
		if i == 0:
			print "x(0) \\\\"
		elif i == 1:
			print "x(T_s) \\\\"
		else:
			print "x(" + str(i) + "T_s) \\\\"
	print "\\end{pmatrix}\n\\end{equation*}"

if __name__ == "__main__":
	n = int(raw_input())
	dftOutput(n)