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from __future__ import print_function, division
from sympy.matrices.expressions import MatrixExpr
from sympy import S, I, sqrt, exp
class DFT(MatrixExpr):
""" Discrete Fourier Transform """
n = property(lambda self: self.args[0])
shape = property(lambda self: (self.n, self.n))
def _entry(self, i, j):
w = exp(-2*S.Pi*I/self.n)
return w**(i*j) / sqrt(self.n)
def _eval_inverse(self):
return IDFT(self.n)
class IDFT(DFT):
""" Inverse Discrete Fourier Transform """
def _entry(self, i, j):
w = exp(-2*S.Pi*I/self.n)
return w**(-i*j) / sqrt(self.n)
def _eval_inverse(self):
return DFT(self.n)
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