基8FFT算法的python代码实现

以下是基于8的FFT算法的Python代码实现：

import math

def twiddle_factor(N):
    W = []
    for i in range(N):
        w = complex(math.cos(2*math.pi*i/N), -math.sin(2*math.pi*i/N))
        W.append(w)
    return W

def fft_8(x):
    N = len(x)
    if N == 1:
        return x
    else:
        x0 = x[::8]
        x1 = x[1::8]
        x2 = x[2::8]
        x3 = x[3::8]
        x4 = x[4::8]
        x5 = x[5::8]
        x6 = x[6::8]
        x7 = x[7::8]
        y0 = fft_8(x0)
        y1 = fft_8(x1)
        y2 = fft_8(x2)
        y3 = fft_8(x3)
        y4 = fft_8(x4)
        y5 = fft_8(x5)
        y6 = fft_8(x6)
        y7 = fft_8(x7)
        W = twiddle_factor(N)
        y = [0]*N
        for i in range(N//8):
            j = 8*i
            y[j] = y0[i] + y1[i]*W[j] + y2[i]*W[2*j] + y3[i]*W[3*j] + y4[i]*W[4*j] + y5[i]*W[5*j] + y6[i]*W[6*j] + y7[i]*W[7*j]
            y[j+1] = y0[i] + y1[i]*W[j+1] + y2[i]*W[2*(j+1)] + y3[i]*W[3*(j+1)] + y4[i]*W[4*(j+1)] + y5[i]*W[5*(j+1)] + y6[i]*W[6*(j+1)] + y7[i]*W[7*(j+1)]
            y[j+2] = y0[i] + y1[i]*W[j+2] + y2[i]*W[2*(j+2)] + y3[i]*W[3*(j+2)] + y4[i]*W[4*(j+2)] + y5[i]*W[5*(j+2)] + y6[i]*W[6*(j+2)] + y7[i]*W[7*(j+2)]
            y[j+3] = y0[i] + y1[i]*W[j+3] + y2[i]*W[2*(j+3)] + y3[i]*W[3*(j+3)] + y4[i]*W[4*(j+3)] + y5[i]*W[5*(j+3)] + y6[i]*W[6*(j+3)] + y7[i]*W[7*(j+3)]
            y[j+4] = y0[i] + y1[i]*W[j+4] + y2[i]*W[2*(j+4)] + y3[i]*W[3*(j+4)] + y4[i]*W[4*(j+4)] + y5[i]*W[5*(j+4)] + y6[i]*W[6*(j+4)] + y7[i]*W[7*(j+4)]
            y[j+5] = y0[i] + y1[i]*W[j+5] + y2[i]*W[2*(j+5)] + y3[i]*W[3*(j+5)] + y4[i]*W[4*(j+5)] + y5[i]*W[5*(j+5)] + y6[i]*W[6*(j+5)] + y7[i]*W[7*(j+5)]
            y[j+6] = y0[i] + y1[i]*W[j+6] + y2[i]*W[2*(j+6)] + y3[i]*W[3*(j+6)] + y4[i]*W[4*(j+6)] + y5[i]*W[5*(j+6)] + y6[i]*W[6*(j+6)] + y7[i]*W[7*(j+6)]
            y[j+7] = y0[i] + y1[i]*W[j+7] + y2[i]*W[2*(j+7)] + y3[i]*W[3*(j+7)] + y4[i]*W[4*(j+7)] + y5[i]*W[5*(j+7)] + y6[i]*W[6*(j+7)] + y7[i]*W[7*(j+7)]
        return y

这段代码实现了基于8的FFT算法，输入的是长度为8的复数序列。其中 twiddle_factor 函数生成旋转因子，fft_8 函数对输入进行递归计算并输出长度为8的DFT结果。