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fftshift

Rearranges an array in a manner similar to Matlab's fftshift function.

Available in version 6.3.0 and later.

Prototype

	function fftshift (
		x        : numeric,  
		mode [1] : integer   
	)

	return_val  :  same size, shape and type as x

Arguments

x

A vector or multidimensional array. If there are two or more dimensions, the two rightmost dimensions will be the rearranged.

mode

Type of rearrangement (shift) to be performed.

Return value

An array of the same size, type and shape as x with the elements rearranged.

Description

See the Matlab description of fftshift. Also, see the examples below.

See Also

reshape, reshape_ind, conform, conform_dims, ndtooned, onedtond

Examples

Example 1

Using fftshift on a vector (i.e., a one-dimensional array).

   f      = (/ 0.0, 0.1,  0.2,  0.3,  0.4, 0.5, -0.5, -0.4, -0.3, -0.2, -0.1 /)
   fshift = fftshift(f, 0)
   print(fshift)

This would yield 0.0 in the middle.

   fshift = (/ -0.5, -0.4, -0.3, -0.2, -0.1,  0.0, 0.1,  0.2,  0.3,  0.4, 0.5/)

Example 2

Using fftshift on an even number of rows and columns:

    nrow  = 6
    ncol  = 6
    N     = nrow*ncol
    a     = onedtond(fspan(1,N,N), (/nrow,ncol/))

    print(" ")
    print("--- Original Array ---")
    write_matrix (x, ncol+"f7.2", False)

    x = fftshift(a, 0)
    print("---mode= 0     quadrant shift")
    write_matrix (x, ncol+"f7.2", False)

    y = fftshift(a, 1)
    print("---mode= 1     column shift")
    write_matrix (y, ncol+"f7.2", False)

    z = fftshift(a,-1)
    print("---mode= -1    row shift")
    write_matrix (y, ncol+"f7.2", False)

This would yield:

           original array: a (6,6)

   1.00   2.00   3.00   4.00   5.00   6.00
   7.00   8.00   9.00  10.00  11.00  12.00
  13.00  14.00  15.00  16.00  17.00  18.00
  19.00  20.00  21.00  22.00  23.00  24.00
  25.00  26.00  27.00  28.00  29.00  30.00
  31.00  32.00  33.00  34.00  35.00  36.00
  
       ---mode= 0     quadrant shift: x
  
  22.00  23.00  24.00  19.00  20.00  21.00
  28.00  29.00  30.00  25.00  26.00  27.00
  34.00  35.00  36.00  31.00  32.00  33.00
   4.00   5.00   6.00   1.00   2.00   3.00
  10.00  11.00  12.00   7.00   8.00   9.00
  16.00  17.00  18.00  13.00  14.00  15.00
  
      ---mode= 1     columns shift: y
  
   4.00   5.00   6.00   1.00   2.00   3.00
  10.00  11.00  12.00   7.00   8.00   9.00
  16.00  17.00  18.00  13.00  14.00  15.00
  22.00  23.00  24.00  19.00  20.00  21.00
  28.00  29.00  30.00  25.00  26.00  27.00
  34.00  35.00  36.00  31.00  32.00  33.00
  
      ---mode=-1     row     shift: z
  
  19.00  20.00  21.00  22.00  23.00  24.00
  25.00  26.00  27.00  28.00  29.00  30.00
  31.00  32.00  33.00  34.00  35.00  36.00
   1.00   2.00   3.00   4.00   5.00   6.00
   7.00   8.00   9.00  10.00  11.00  12.00
  13.00  14.00  15.00  16.00  17.00  18.00

==================================================

Example 3

Using fftshift on an even number of rows and an odd number of columns:

    nrow  = 6
    ncol  = 5
    N     = nrow*ncol

The results are:

	--- Original Array (6,5) ---
  
   1.00   2.00   3.00   4.00   5.00
   6.00   7.00   8.00   9.00  10.00
  11.00  12.00  13.00  14.00  15.00
  16.00  17.00  18.00  19.00  20.00
  21.00  22.00  23.00  24.00  25.00
  26.00  27.00  28.00  29.00  30.00
  
	---mode= 0     quadrant shift
  
  19.00  20.00  16.00  17.00  18.00
  24.00  25.00  21.00  22.00  23.00
  29.00  30.00  26.00  27.00  28.00
   4.00   5.00   1.00   2.00   3.00
   9.00  10.00   6.00   7.00   8.00
  14.00  15.00  11.00  12.00  13.00
	 
	---mode= 1     column shift
  
   4.00   5.00   1.00   2.00   3.00
   9.00  10.00   6.00   7.00   8.00
  14.00  15.00  11.00  12.00  13.00
  19.00  20.00  16.00  17.00  18.00
  24.00  25.00  21.00  22.00  23.00
  29.00  30.00  26.00  27.00  28.00
	 
	---mode=-1     row    shift
  
  16.00  17.00  18.00  19.00  20.00
  21.00  22.00  23.00  24.00  25.00
  26.00  27.00  28.00  29.00  30.00
   1.00   2.00   3.00   4.00   5.00
   6.00   7.00   8.00   9.00  10.00
  11.00  12.00  13.00  14.00  15.00

Example 4

Using fftshift on an odd number of rows and an even number of columns:

    nrow  = 5
    ncol  = 6
    N     = nrow*ncol

The results are:

	--- Original Array (5,6)---

	 
   1.00   2.00   3.00   4.00   5.00   6.00
   7.00   8.00   9.00  10.00  11.00  12.00
  13.00  14.00  15.00  16.00  17.00  18.00
  19.00  20.00  21.00  22.00  23.00  24.00
  25.00  26.00  27.00  28.00  29.00  30.00
	 
	---mode=0     quadrant shift
  
  22.00  23.00  24.00  19.00  20.00  21.00
  28.00  29.00  30.00  25.00  26.00  27.00
   4.00   5.00   6.00   1.00   2.00   3.00
  10.00  11.00  12.00   7.00   8.00   9.00
  16.00  17.00  18.00  13.00  14.00  15.00
	 
	---mode=1     column shift
	 
   4.00   5.00   6.00   1.00   2.00   3.00
  10.00  11.00  12.00   7.00   8.00   9.00
  16.00  17.00  18.00  13.00  14.00  15.00
  22.00  23.00  24.00  19.00  20.00  21.00
  28.00  29.00  30.00  25.00  26.00  27.00
  
	---mode=-1     row    shift
  
  19.00  20.00  21.00  22.00  23.00  24.00
  25.00  26.00  27.00  28.00  29.00  30.00
   1.00   2.00   3.00   4.00   5.00   6.00
   7.00   8.00   9.00  10.00  11.00  12.00
  13.00  14.00  15.00  16.00  17.00  18.00

Example 5

Using fftshift on an odd number of rows and columns:

    nrow  = 5
    ncol  = 5
    N     = nrow*ncol

The results are:

	--- Original Array ---
  
   1.00   2.00   3.00   4.00   5.00
   6.00   7.00   8.00   9.00  10.00
  11.00  12.00  13.00  14.00  15.00
  16.00  17.00  18.00  19.00  20.00
  21.00  22.00  23.00  24.00  25.00
	 
	---mode= 0     quadrant shift
  
  19.00  20.00  16.00  17.00  18.00
  24.00  25.00  21.00  22.00  23.00
   4.00   5.00   1.00   2.00   3.00
   9.00  10.00   6.00   7.00   8.00
  14.00  15.00  11.00  12.00  13.00
	 
	---mode= 1     column shift
  
   4.00   5.00   1.00   2.00   3.00
   9.00  10.00   6.00   7.00   8.00
  14.00  15.00  11.00  12.00  13.00
  19.00  20.00  16.00  17.00  18.00
  24.00  25.00  21.00  22.00  23.00
	 
	---mode=-1     row    shift
  
  16.00  17.00  18.00  19.00  20.00
  21.00  22.00  23.00  24.00  25.00
   1.00   2.00   3.00   4.00   5.00
   6.00   7.00   8.00   9.00  10.00
  11.00  12.00  13.00  14.00  15.00