DFT_slow and FFT

import numpy as np

def DFT_slow(x):
    x = np.asarray(x, dtype=float)
    N = x.shape[0]
    n = np.arange(N)
    k = n.reshape((N, 1))
    M = np.exp(-2j * np.pi * k * n / N)
    return np.dot(M, x)

def FFT(x):
    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 <= 4:  # 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])