我使用这段 python 代码将数据转换为傅里叶相位和幅度，然后检索原始数据。

from random import randint as RI
import numpy.fft as FFT
import math

w = 4
h = 4
random_range = 255

vals = [[] for i in range(h)]

for i in range(h):
    for j in range(w):
        vals[i].append(RI(0,random_range))

fftc = FFT.fft2(vals) 

magnitudes = [[] for i in range(h)]
phases = [[] for i in range(h)]

for i in range(h):
    for j in range(w):
        magnitudes[i].append(math.sqrt(fftc[i][j].real**2+fftc[i][j].imag**2))
        phases[i].append(math.atan(fftc[i][j].imag/fftc[i][j].real))

for_ifft = [[] for i in range(h)]

for i in range(h):
    for j in range(w):
        rl = magnitudes[i][j]*math.cos(phases[i][j])
        im = magnitudes[i][j]*math.sin(phases[i][j])
        for_ifft[i].append(complex(rl,im))


ifftc = FFT.ifft2(for_ifft)


print vals
print ifftc

当我比较输出时，结果是不同的。例如，两个典型的输出是：

//original data
[[115, 4, 33, 91], [228, 123, 46, 111], [83, 227, 81, 55], [229, 188, 138, 41]]

//retrieved data from phase and magnitude informations
[[ 309,182.25,105,57.25],[ 33,118.75,120.50,116.25],[ 148,128.75,79,94.75],[ 165,112.25,-6.50,29.75]]

我知道它背后的理论。例如，为了计算相位和幅度，我们这样做：

Magnitude = Square_Root(real*real+imaginary*imaginary)
Phase = Inverse_Tangent(imaginary/real)

为了从幅度和相位计算复数，我们这样做：

Real = Magnitude * cos(Phase)
Imaginary = Magnitude * sin(Phase)

那么，问题的原因是什么。是否是数据扩展问题。