用python写一个FFT代码

以下是Python中的FFT代码：

import numpy as np

def fft(x):
    """
    FFT (Fast Fourier Transform) algorithm
    """
    # Check if input is a power of 2
    n = len(x)
    if n == 1:
        return x
    if n % 2 > 0:
        raise ValueError("Size of x must be a power of 2")
    
    # Divide the signal into even and odd components
    even = fft(x[::2])
    odd = fft(x[1::2])
    
    # Calculate the Fourier coefficients
    factor = np.exp(-2j * np.pi * np.arange(n) / n)
    return np.concatenate([even + factor[:int(n / 2)] * odd,
                           even + factor[int(n / 2):] * odd])

# Test the FFT function with a sine wave
x = np.linspace(0, 2*np.pi, 8)
y = np.sin(x)
print("Input signal: ", y)
print("FFT: ", fft(y))

该代码使用递归地将信号分解为偶数和奇数分量，并使用指数函数计算傅里叶系数。最后，它将偶数和奇数分量的结果合并为最终结果。