fft2rm.d

用c语言实现了图像二维快速傅里叶变换

The original data, Ak:
   0,   0:     0.021005544, 0.00000000e+000
   0,   1:     0.020311225, 0.00000000e+000
   0,   2:     0.019820188, 0.00000000e+000
   0,   3:     0.019527518, 0.00000000e+000
   0,   4:     0.019430285, 0.00000000e+000
   0,   5:     0.019527518, 0.00000000e+000
   0,   6:     0.019820188, 0.00000000e+000
   0,   7:     0.020311225, 0.00000000e+000
   1,   0:     0.020311225, 0.00000000e+000
   1,   1:     0.019639856, 0.00000000e+000
   1,   2:     0.019165050, 0.00000000e+000
   1,   3:     0.018882053, 0.00000000e+000
   1,   4:     0.018788035, 0.00000000e+000
   1,   5:     0.018882053, 0.00000000e+000
   1,   6:     0.019165050, 0.00000000e+000
   1,   7:     0.019639856, 0.00000000e+000
   2,   0:     0.019820188, 0.00000000e+000
   2,   1:     0.019165050, 0.00000000e+000
   2,   2:     0.018701722, 0.00000000e+000
   2,   3:     0.018425567, 0.00000000e+000
   2,   4:     0.018333822, 0.00000000e+000
   2,   5:     0.018425567, 0.00000000e+000
   2,   6:     0.018701722, 0.00000000e+000
   2,   7:     0.019165050, 0.00000000e+000
   3,   0:     0.019527518, 0.00000000e+000
   3,   1:     0.018882053, 0.00000000e+000
   3,   2:     0.018425567, 0.00000000e+000
   3,   3:     0.018153490, 0.00000000e+000
   3,   4:     0.018063099, 0.00000000e+000
   3,   5:     0.018153490, 0.00000000e+000
   3,   6:     0.018425567, 0.00000000e+000
   3,   7:     0.018882053, 0.00000000e+000
   4,   0:     0.019430285, 0.00000000e+000
   4,   1:     0.018788035, 0.00000000e+000
   4,   2:     0.018333822, 0.00000000e+000
   4,   3:     0.018063099, 0.00000000e+000
   4,   4:     0.017973159, 0.00000000e+000
   4,   5:     0.018063099, 0.00000000e+000
   4,   6:     0.018333822, 0.00000000e+000
   4,   7:     0.018788035, 0.00000000e+000
   5,   0:     0.019527518, 0.00000000e+000
   5,   1:     0.018882053, 0.00000000e+000
   5,   2:     0.018425567, 0.00000000e+000
   5,   3:     0.018153490, 0.00000000e+000
   5,   4:     0.018063099, 0.00000000e+000
   5,   5:     0.018153490, 0.00000000e+000
   5,   6:     0.018425567, 0.00000000e+000
   5,   7:     0.018882053, 0.00000000e+000
   6,   0:     0.019820188, 0.00000000e+000
   6,   1:     0.019165050, 0.00000000e+000
   6,   2:     0.018701722, 0.00000000e+000
   6,   3:     0.018425567, 0.00000000e+000
   6,   4:     0.018333822, 0.00000000e+000
   6,   5:     0.018425567, 0.00000000e+000
   6,   6:     0.018701722, 0.00000000e+000
   6,   7:     0.019165050, 0.00000000e+000
   7,   0:     0.020311225, 0.00000000e+000
   7,   1:     0.019639856, 0.00000000e+000
   7,   2:     0.019165050, 0.00000000e+000
   7,   3:     0.018882053, 0.00000000e+000
   7,   4:     0.018788035, 0.00000000e+000
   7,   5:     0.018882053, 0.00000000e+000
   7,   6:     0.019165050, 0.00000000e+000
   7,   7:     0.019639856, 0.00000000e+000
FFT, direct transform ( A -> x ), x:
   0,   0:     1.214976455, 0.00000000e+000
   0,   1:     0.020409532,-1.90819582e-017
   0,   2:     0.006049673, 5.55128453e-017
   0,   3:     0.003551140,-1.90819582e-017
   0,   4:     0.003032386, 0.00000000e+000
   0,   5:     0.003551140, 1.90819582e-017
   0,   6:     0.006049673,-5.55128453e-017
   0,   7:     0.020409532, 1.90819582e-017
   1,   0:     0.020460471, 0.00000000e+000
   1,   1:     0.000201249, 2.01249220e-004
   1,   2:     0.000000000, 0.00000000e+000
   1,   3:    -0.000083360,-8.33601562e-005
   1,   4:     0.000000000, 0.00000000e+000
   1,   5:     0.000201249, 2.01249220e-004
   1,   6:     0.000203248, 2.03248371e-004
   1,   7:     0.000485859, 4.85858596e-004
   2,   0:     0.006064772, 0.00000000e+000
   2,   1:     0.000059653, 5.96531025e-005
   2,   2:     0.000000000, 0.00000000e+000
   2,   3:    -0.000024709,-2.47091241e-005
   2,   4:     0.000000000, 0.00000000e+000
   2,   5:     0.000059653, 5.96531025e-005
   2,   6:     0.000060246, 6.02456791e-005
   2,   7:     0.000144015, 1.44015329e-004
   3,   0:     0.003560003, 0.00000000e+000
   3,   1:     0.000035016, 3.50161984e-005
   3,   2:     0.000000000, 0.00000000e+000
   3,   3:    -0.000014504,-1.45041843e-005
   3,   4:     0.000000000, 0.00000000e+000
   3,   5:     0.000035016, 3.50161984e-005
   3,   6:     0.000035364, 3.53640391e-005
   3,   7:     0.000084537, 8.45365811e-005
   4,   0:     0.003039954, 0.00000000e+000
   4,   1:     0.020409532, 1.90819582e-017
   4,   2:     0.006049673,-5.55128453e-017
   4,   3:     0.003551140, 1.90819582e-017
   4,   4:     0.003032386, 0.00000000e+000
   4,   5:     0.003551140,-1.90819582e-017
   4,   6:     0.006049673, 5.55128453e-017
   4,   7:     0.020409532,-1.90819582e-017
   5,   0:     0.003560003, 0.00000000e+000
   5,   1:     0.000084537,-8.45365811e-005
   5,   2:     0.000035364,-3.53640391e-005
   5,   3:     0.000035016,-3.50161984e-005
   5,   4:     0.000000000, 0.00000000e+000
   5,   5:    -0.000014504, 1.45041843e-005
   5,   6:     0.000000000, 0.00000000e+000
   5,   7:     0.000035016,-3.50161984e-005
   6,   0:     0.006064772, 0.00000000e+000
   6,   1:     0.000144015,-1.44015329e-004
   6,   2:     0.000060246,-6.02456791e-005
   6,   3:     0.000059653,-5.96531025e-005
   6,   4:     0.000000000, 0.00000000e+000
   6,   5:    -0.000024709, 2.47091241e-005
   6,   6:     0.000000000, 0.00000000e+000
   6,   7:     0.000059653,-5.96531025e-005
   7,   0:     0.020460471, 0.00000000e+000
   7,   1:     0.000485859,-4.85858596e-004
   7,   2:     0.000203248,-2.03248371e-004
   7,   3:     0.000201249,-2.01249220e-004
   7,   4:     0.000000000, 0.00000000e+000
   7,   5:    -0.000083360, 8.33601562e-005
   7,   6:     0.000000000, 0.00000000e+000
   7,   7:     0.000201249,-2.01249220e-004
IFFT, inverse transform ( x -> A ), A:
   0,   0:     1.214976455, 0.00000000e+000
   0,   1:     0.020409532, 0.00000000e+000
   0,   2:     0.006049673, 0.00000000e+000
   0,   3:     0.003551140, 0.00000000e+000
   0,   4:     0.003032386, 0.00000000e+000
   0,   5:     0.003551140, 0.00000000e+000
   0,   6:     0.006049673, 0.00000000e+000
   0,   7:     0.020409532, 0.00000000e+000
   1,   0:     0.020460471, 0.00000000e+000
   1,   1:     0.000343554, 3.43553908e-004
   1,   2:     0.000101624, 1.01624185e-004
   1,   3:     0.000058945, 5.89445318e-005
   1,   4:     0.000000000, 0.00000000e+000
   1,   5:     0.000058945, 5.89445318e-005
   1,   6:     0.000101624, 1.01624185e-004
   1,   7:     0.000343554, 3.43553908e-004
   2,   0:     0.006064772, 0.00000000e+000
   2,   1:     0.000101834, 1.01834216e-004
   2,   2:     0.000030123, 3.01228395e-005
   2,   3:     0.000017472, 1.74719892e-005
   2,   4:     0.000000000, 0.00000000e+000
   2,   5:     0.000017472, 1.74719892e-005
   2,   6:     0.000030123, 3.01228395e-005
   2,   7:     0.000101834, 1.01834216e-004
   3,   0:     0.003560003, 0.00000000e+000
   3,   1:     0.000059776, 5.97763897e-005
   3,   2:     0.000017682, 1.76820196e-005
   3,   3:     0.000010256, 1.02560071e-005
   3,   4:     0.000000000, 0.00000000e+000
   3,   5:     0.000010256, 1.02560071e-005
   3,   6:     0.000017682, 1.76820196e-005
   3,   7:     0.000059776, 5.97763897e-005
   4,   0:     0.003039954, 0.00000000e+000
   4,   1:     0.020409532, 0.00000000e+000
   4,   2:     0.006049673, 0.00000000e+000
   4,   3:     0.003551140, 0.00000000e+000
   4,   4:     0.003032386, 0.00000000e+000
   4,   5:     0.003551140, 0.00000000e+000
   4,   6:     0.006049673, 0.00000000e+000
   4,   7:     0.020409532, 0.00000000e+000
   5,   0:     0.003560003, 0.00000000e+000
   5,   1:     0.000059776,-5.97763897e-005
   5,   2:     0.000017682,-1.76820196e-005
   5,   3:     0.000010256,-1.02560071e-005
   5,   4:     0.000000000, 0.00000000e+000
   5,   5:     0.000010256,-1.02560071e-005
   5,   6:     0.000017682,-1.76820196e-005
   5,   7:     0.000059776,-5.97763897e-005
   6,   0:     0.006064772, 0.00000000e+000
   6,   1:     0.000101834,-1.01834216e-004
   6,   2:     0.000030123,-3.01228395e-005
   6,   3:     0.000017472,-1.74719892e-005
   6,   4:     0.000000000, 0.00000000e+000
   6,   5:     0.000017472,-1.74719892e-005
   6,   6:     0.000030123,-3.01228395e-005
   6,   7:     0.000101834,-1.01834216e-004
   7,   0:     0.020460471, 0.00000000e+000
   7,   1:     0.000343554,-3.43553908e-004
   7,   2:     0.000101624,-1.01624185e-004
   7,   3:     0.000058945,-5.89445318e-005
   7,   4:     0.000000000, 0.00000000e+000
   7,   5:     0.000058945,-5.89445318e-005
   7,   6:     0.000101624,-1.01624185e-004
   7,   7:     0.000343554,-3.43553908e-004