请帮我用python写一个FFT程序

我可以为你提供一个简单的FFT程序的python代码：

import numpy as np

def fft(x):
"""A recursive implementation of the 1D Cooley-Tukey FFT"""
x = np.asarray(x, dtype=float)
N = x.shape[0]

if N % 2 > 0:
raise ValueError("size of x must be a power of 2")
elif N <= 32: # this cutoff should be optimized
return dft_slow(x)
else:
X_even = fft(x[::2])
X_odd = fft(x[1::2])
factor = np.exp(-2j * np.pi * np.arange(N) / N)
return np.concatenate([X_even + factor[:N // 2] * X_odd,
X_even + factor[N // 2:] * X_odd])