应用于矩阵的fft / fft2的返回值有什么区别？

Question

在下面的程序中，我想计算由U给出的给定字段的快速傅里叶变换.fft和fft2的返回值之间有什么区别？任何帮助，将不胜感激！谢谢。

import numpy as np
from numpy import sin, cos, pi

nx=3
ny=3

px=2*pi
py=2*pi

qx=1.0*px/(nx-1)
qy=1.0*py/(ny-1)

x = np.linspace(0,px,nx)
y = np.linspace(0,py,ny)

X,Y = np.meshgrid(x,y)

U=cos(X)*sin(Y)

#compite fft's
Uh1=np.fft.fft(U)

Uh2=np.fft.fft2(U)

print('For fft')
print(Uh1)

print('For fft2')
print(Uh2)

#What is the difference between Uh1 and Uh2? Thank you!

这是我得到的：

For fft
[[  0.00000000e+00 +0.00000000e+00j   0.00000000e+00 +0.00000000e+00j
0.00000000e+00 +0.00000000e+00j]
[  1.22464680e-16 +0.00000000e+00j   1.22464680e-16 +2.12115048e-16j
1.22464680e-16 -2.12115048e-16j]
[ -2.44929360e-16 +0.00000000e+00j  -2.44929360e-16 -4.24230095e-16j
-2.44929360e-16 +4.24230095e-16j]]
For fft2
[[ -1.22464680e-16 +0.00000000e+00j  -1.22464680e-16 -2.12115048e-16j
-1.22464680e-16 +2.12115048e-16j]
[  6.12323400e-17 -3.18172572e-16j   6.12323400e-16 -2.12115048e-16j
-4.89858720e-16 -4.24230095e-16j]
[  6.12323400e-17 +3.18172572e-16j  -4.89858720e-16 +4.24230095e-16j
6.12323400e-16 +2.12115048e-16j]]

谢谢！

Answer 1

np.fft模块的docstring。

Standard FFTs
-------------

.. autosummary::
   :toctree: generated/

   fft       Discrete Fourier transform.
   ifft      Inverse discrete Fourier transform.
   fft2      Discrete Fourier transform in two dimensions.
   ifft2     Inverse discrete Fourier transform in two dimensions.
   fftn      Discrete Fourier transform in N-dimensions.
   ifftn     Inverse discrete Fourier transform in N dimensions.

如果您想要想象差异，那么绘制这两个基质会给出这个。我对fft的了解不够，甚至不知道以这种方式绘制它们是否有意义。

plt.figure()

plt.subplot(2,2,1)
plt.plot(Uh1.real.ravel())
plt.title("1 - real")
plt.subplot(2,2,2)
plt.plot(Uh2.real.ravel())
plt.title("2 - real")

plt.subplot(2,2,3)
plt.plot(Uh1.imag.ravel())
plt.title("1 - imaginary")
plt.subplot(2,2,4)
plt.plot(Uh2.imag.ravel())
plt.title("2 - imaginary")

plt.figure()

plt.subplot(2,2,1)
plt.hist(Uh1.real.ravel())
plt.title("1 - real")
plt.subplot(2,2,2)
plt.hist(Uh2.real.ravel())
plt.title("2 - real")

plt.subplot(2,2,3)
plt.hist(Uh1.imag.ravel())
plt.title("1 - imaginary")
plt.subplot(2,2,4)
plt.hist(Uh2.imag.ravel())
plt.title("2 - imaginary")