基2的FFT算法 | Python实现

***************************************************************
# 与scipy库里的fft作比较
***************************************************************
import numpy as np
import math
from scipy.fftpack import fft

def my_fft(x, N):
    """
    实现FFT
    
    x: 离散序列
    N: x的长度
    """
    
    # 反序排列
    F = np.array(x)
    LH = int(N / 2)
    J = LH
    # print(J)
    M = N - 2
    for I in range(1, M+1):
        if I < J:
            T = F[I]
            F[I] = F[J]
            F[J] = T
        K = LH
        while J >= K:
            J = int(J - K)
            K = int(K / 2)
        J = J + K
    
    # 蝶形运算
    ls = [i for i in range(int(N/2))]
    a = np.array(ls)
    Wmn = np.exp(-1j * 2 * math.pi * a / N)
    Wmn = list(Wmn)
    F = list(F)
    n1 = 1
    n2 = 1
    group = N
    for k in range(1, K+1):
        n2 = n1
        n1 = n2 * 2
        group = int(group / 2)
        for j in range(1, group+1):
            h = (j-1) * n1 + 1
            for m in range(h, h+n2):
                W1 = Wmn[int((m-h) * N / n1)]
                W = W1 * F[m + n2 - 1]
                F[m + n2 - 1] = F[m - 1] - W
                F[m - 1] = complex(F[m - 1]) + W
    return F
    
    
test_series = [3, 2, 6, 8, 10, 22, 1, 2]
N = len(test_series)
F1 = my_fft(test_series, N)    # 我的fft
print("my_fft:",np.array(F1))

print("------------------------------------------------------------")

F2 = fft(test_series)          # scipy的fft
print("scipy_fft:", F2)


"""
my_fft: [ 54.         +0.j         -25.38477631 +4.89949494j
  6.        -14.j          11.38477631+14.89949494j
-14.         +0.j          11.38477631-14.89949494j
  6.        +14.j         -25.38477631 -4.89949494j]
------------------------------------------------------------
scipy_fft: [ 54.         -0.j         -25.38477631 +4.89949494j
   6.        -14.j          11.38477631+14.89949494j
 -14.         -0.j          11.38477631-14.89949494j
   6.        +14.j         -25.38477631 -4.89949494j]
"""