matlab移位操作函数之circshift + fftshift + ifftshift

循环移位函数circshift

circshift Shift positions of elements circularly.
Y = circshift(X,K) where K is an integer scalar circularly shifts
the elements in the array X by K positions along the first dimension.
If K is positive, the values of X are shifted down in row direction or shifted right in col direction.
If it is negative, the values of X are shifted up in row direction or shifted left in col direction.

• 注： 移位参数K的正负方向与图像坐标系的方向相同，大于0表示沿x轴向右或沿y轴下移，小于0表示沿x轴向左或沿y轴上移

matlab举例说明

Y = circshift(X,K,DIM) circularly shifts along the dimension DIM.
 
Y = circshift(X,V) circularly shifts the values in the array X
by V elements. V is a vector of integers where the N-th element 
specifies the shift amount along the N-th dimension of
array X. 
 
Examples:
   A = [ 1 2 3;4 5 6; 7 8 9];
   % circularly shifts first dimension values down by 1.
   B = circshift(A,1) % 沿y轴向下移一位
   B =     7     8     9
           1     2     3
           4     5     6
   % 沿行向下移一位之后，再向左移一位
   B = circshift(A,[1 -1]) % circularly shifts first dimension values
                           % down by 1 and second dimension left by 1.
   B =     8     9     7
           2     3     1
           5     6     4
 
沿x或y轴翻转 类似cv2.filp()操作
A = [ 1 2 3; 4 5 6; 7 8 9];
B = A(:,end:-1:1) %沿垂直方向Y轴翻转
% B = A(end:-1:1, :) %沿水平方向X轴翻转
C = circshift(B,[0,1]) %翻转之后再进行列移位，右移1位
B = 
     3     2     1
     6     5     4
     9     8     7
C = 
     1     3     2
     4     6     5
     7     9     8

fftshift + ifftshift

>> help fftshift
 fftshift Shift zero-frequency component to center of spectrum.
 将频率在0附近的成分移到频谱的中心
    For vectors, fftshift(X) swaps the left and right halves of
    X.  For matrices, fftshift(X) swaps the first and third
    quadrants and the second and fourth quadrants.  For N-D
    arrays, fftshift(X) swaps "half-spaces" of X along each
    dimension.
 
    fftshift(X,DIM) applies the fftshift operation along the 
    dimension DIM.
 
    fftshift is useful for visualizing the Fourier transform with
    the zero-frequency component in the middle of the spectrum.
 
    Class support for input X:
       float: double, single
 
    See also ifftshift, fft, fft2, fftn, circshift.


>> help ifftshift %% ifftshift undoes the effects of FFTSHIFT.对傅里叶变换平移的撤销
 ifftshift Inverse FFT shift.
    For vectors, ifftshift(X) swaps the left and right halves of
    X.  For matrices, ifftshift(X) swaps the first and third
    quadrants and the second and fourth quadrants.  For N-D
    arrays, ifftshift(X) swaps "half-spaces" of X along each
    dimension.
 
    ifftshift(X,DIM) applies the ifftshift operation along the 
    dimension DIM.
 
    Class support for input X: 
       float: double, single
 
    See also fftshift, fft, fft2, fftn, circshift.

    ifftshift will undo the results of fftshift. If the matrix X contains an odd number of elements, ifftshift(fftshift(X)) must be done to obtain the original X. Simply performing fftshift(X) twice will not produce X.
    

• 傅里叶变换平移函数fftshift的本质是当移位的大小为输入矩阵行列的1/2时，循环移位的操作；即将输入矩阵分为四个象限，第1和3象限互换，第2和4象限互换，如下图所示
• 逆傅里叶变换平移函数ifftshift是fftshift操作的逆向还原操作；
• 注意的是：当输入矩阵的行列为奇数时，调用circshift函数时，将输入参数除以2，向下取整后等价于fftshift操作；向上取整等价于ifftshift操作

	//execute the fftshift operation
	int xShift = (int)(input.cols / 2.0);
	int yShift = (int)(input.rows / 2.0);

	cv::Mat fftshift;
	CircShiftFunc(input, fftshift, xShift, yShift);
	
    //execute the ifftshift operation
	cv::Mat ifftMat;