将FFT函数从Python 2.x转换为Python 3.x，并从中计算IFFT

Question

I have an Fast Fourier Transform function in Python for versions 2.x. I want to make it in Python 3.x, but I have some problems with "xrange" and list identifiers(as my compiler said). I also have no idea how to compute Inversed FFT from my FFT without using of any non-standard libraries. Code is below. Thanks in advance...

 from cmath import exp,pi

 def FFT(X):
  n = len(X)
  w = exp(-2*pi*1j/n)
  if n > 1:
    X = FFT(X[::2]) + FFT(X[1::2])
    for k in xrange(n/2):
        xk = X[k]
        X[k] = xk + w**k*X[k+n/2]
        X[k+n/2] = xk - w**k*X[k+n/2]
 return X 

UPD: Totally reconstructed ,my FFT and constructed IFFT due to your advices. PS How to close post?

Answer 1

There are a couple ways to convert your FFT into an IFFT. The easiest is to get rid of the minus sign inside the parameter to your exp() function for w. The next is to take the complex conjugate of the FFT of the complex conjugate of the input.

If you don't scale your forward FFT, then common practice is to scale your IFFT computation by 1/N (the length), so that IFFT(FFT()) results in the same total sum magnitude. If you do scale your FFT by 1/N, then don't scale your IFFT computation. Or scale both by 1/sqrt(N).