test_fft2.m
sin 2 th data
0 real = 0, imag = 0
1 real = 0.70711, imag = 0
2 real = 1, imag = 0
3 real = 0.70711, imag = 0
4 real = 1.2246e-016, imag = 0
5 real = -0.70711, imag = 0
6 real = -1, imag = 0
7 real = -0.70711, imag = 0
8 real = -2.4493e-016, imag = 0
9 real = 0.70711, imag = 0
10 real = 1, imag = 0
11 real = 0.70711, imag = 0
12 real = 3.6739e-016, imag = 0
13 real = -0.70711, imag = 0
14 real = -1, imag = 0
15 real = -0.70711, imag = 0
sin 2 th FFT
0 cos = -6.4325e-016, sin = 0
1 cos = -8.3785e-016, sin = 2.1275e-016
2 cos = -1.9909e-015, sin = -8
3 cos = 1.1183e-015, sin = -1.193e-015
4 cos = 2.4493e-016, sin = 0
5 cos = -6.2844e-016, sin = -7.031e-016
6 cos = 5.2129e-016, sin = -1.7764e-015
7 cos = 1.3277e-015, sin = -2.7711e-016
8 cos = 1.1331e-015, sin = 0
9 cos = 1.3277e-015, sin = 2.7711e-016
10 cos = 5.2129e-016, sin = 1.7764e-015
11 cos = -6.2844e-016, sin = 7.031e-016
12 cos = 2.4493e-016, sin = 0
13 cos = 1.1183e-015, sin = 1.193e-015
14 cos = -1.9909e-015, sin = 8
15 cos = -8.3785e-016, sin = -2.1275e-016
antialias and normalize sin 2 th FFT
0 cos = -4.0203e-017, sin = 0
1 cos = -1.0473e-016, sin = -2.6594e-017
2 cos = -2.4886e-016, sin = 1
3 cos = 1.3979e-016, sin = 1.4912e-016
4 cos = 3.0616e-017, sin = 0
5 cos = -7.8554e-017, sin = 8.7887e-017
6 cos = 6.5161e-017, sin = 2.2204e-016
7 cos = 1.6596e-016, sin = 3.4638e-017
 
 
cos 2 th data
0 real = 1, imag = 0
1 real = 0.70711, imag = 0
2 real = 6.1232e-017, imag = 0
3 real = -0.70711, imag = 0
4 real = -1, imag = 0
5 real = -0.70711, imag = 0
6 real = -1.837e-016, imag = 0
7 real = 0.70711, imag = 0
8 real = 1, imag = 0
9 real = 0.70711, imag = 0
10 real = 3.0616e-016, imag = 0
11 real = -0.70711, imag = 0
12 real = -1, imag = 0
13 real = -0.70711, imag = 0
14 real = -4.2863e-016, imag = 0
15 real = 0.70711, imag = 0
cos 2 th FFT
0 cos = 1.9916e-016, sin = 0
1 cos = -1.2519e-015, sin = 9.7594e-016
2 cos = 8, sin = -2.5498e-015
3 cos = 2.1163e-016, sin = -1.1253e-015
4 cos = 2.4493e-016, sin = -4.4409e-016
5 cos = 4.8113e-016, sin = -1.1253e-015
6 cos = 1.3323e-015, sin = -5.9038e-016
7 cos = 5.5916e-016, sin = 9.7594e-016
8 cos = -6.8902e-016, sin = 0
9 cos = 5.5916e-016, sin = -9.7594e-016
10 cos = 1.3323e-015, sin = 5.9038e-016
11 cos = 4.8113e-016, sin = 1.1253e-015
12 cos = 2.4493e-016, sin = 4.4409e-016
13 cos = 2.1163e-016, sin = 1.1253e-015
14 cos = 8, sin = 2.5498e-015
15 cos = -1.2519e-015, sin = -9.7594e-016
antialias and normalize cos 2 th FFT
0 cos = 1.2447e-017, sin = 0
1 cos = -1.5649e-016, sin = -1.2199e-016
2 cos = 1, sin = 3.1873e-016
3 cos = 2.6454e-017, sin = 1.4066e-016
4 cos = 3.0616e-017, sin = 5.5511e-017
5 cos = 6.0141e-017, sin = 1.4066e-016
6 cos = 1.6653e-016, sin = 7.3797e-017
7 cos = 6.9895e-017, sin = -1.2199e-016
 
 
1.0 + cos 2 th data
0 real = 2, imag = 0
1 real = 1.7071, imag = 0
2 real = 1, imag = 0
3 real = 0.29289, imag = 0
4 real = 0, imag = 0
5 real = 0.29289, imag = 0
6 real = 1, imag = 0
7 real = 1.7071, imag = 0
8 real = 2, imag = 0
9 real = 1.7071, imag = 0
10 real = 1, imag = 0
11 real = 0.29289, imag = 0
12 real = 0, imag = 0
13 real = 0.29289, imag = 0
14 real = 1, imag = 0
15 real = 1.7071, imag = 0
1.0 + cos 2 th FFT
0 cos = 16, sin = 0
1 cos = -1.4247e-015, sin = 9.7594e-016
2 cos = 8, sin = -1.9222e-015
3 cos = 9.4297e-017, sin = -1.1253e-015
4 cos = 8.8818e-016, sin = 0
5 cos = 5.3374e-016, sin = -1.1253e-015
6 cos = 1.3323e-015, sin = -5.8994e-016
7 cos = 7.9667e-016, sin = 9.7594e-016
8 cos = -8.8818e-016, sin = 0
9 cos = 7.9667e-016, sin = -9.7594e-016
10 cos = 1.3323e-015, sin = 5.8994e-016
11 cos = 5.3374e-016, sin = 1.1253e-015
12 cos = 8.8818e-016, sin = 0
13 cos = 9.4297e-017, sin = 1.1253e-015
14 cos = 8, sin = 1.9222e-015
15 cos = -1.4247e-015, sin = -9.7594e-016
antialias and normalize 1.0 + cos 2 th FFT
0 cos = 1, sin = 0
1 cos = -1.7809e-016, sin = -1.2199e-016
2 cos = 1, sin = 2.4028e-016
3 cos = 1.1787e-017, sin = 1.4066e-016
4 cos = 1.1102e-016, sin = 0
5 cos = 6.6717e-017, sin = 1.4066e-016
6 cos = 1.6653e-016, sin = 7.3743e-017
7 cos = 9.9583e-017, sin = -1.2199e-016
 
 
square wave data, cos series
0 real = 1, imag = 0
1 real = 1, imag = 0
2 real = 1, imag = 0
3 real = 1, imag = 0
4 real = 0, imag = 0
5 real = -1, imag = 0
6 real = -1, imag = 0
7 real = -1, imag = 0
8 real = -1, imag = 0
9 real = -1, imag = 0
10 real = -1, imag = 0
11 real = -1, imag = 0
12 real = 0, imag = 0
13 real = 1, imag = 0
14 real = 1, imag = 0
15 real = 1, imag = 0
square wave generate, using cos
0 real = 1.0353
1 real = 1.0263
2 real = 0.99731
3 real = 0.92884
4 real = 7.5104e-016
5 real = -0.92884
6 real = -0.99731
7 real = -1.0263
8 real = -1.0353
9 real = -1.0263
10 real = -0.99731
11 real = -0.92884
12 real = -2.4362e-015
13 real = 0.92884
14 real = 0.99731
15 real = 1.0263
0 real = 1, imag = 0
1 real = 1, imag = 0
2 real = 1, imag = 0
3 real = 1, imag = 0
4 real = 0, imag = 0
5 real = -1, imag = 0
6 real = -1, imag = 0
7 real = -1, imag = 0
8 real = -1, imag = 0
9 real = -1, imag = 0
10 real = -1, imag = 0
11 real = -1, imag = 0
12 real = 0, imag = 0
13 real = 1, imag = 0
14 real = 1, imag = 0
15 real = 1, imag = 0
square wave FFT cos series
0 cos = 0, sin = 0
1 cos = 10.0547, sin = 0
2 cos = 0, sin = 0
3 cos = -2.9932, sin = 0
4 cos = 0, sin = 0
5 cos = 1.3364, sin = 0
6 cos = 0, sin = 0
7 cos = -0.39782, sin = 0
8 cos = 0, sin = 0
9 cos = -0.39782, sin = 0
10 cos = 0, sin = 0
11 cos = 1.3364, sin = 0
12 cos = 0, sin = 0
13 cos = -2.9932, sin = 0
14 cos = 0, sin = 0
15 cos = 10.0547, sin = 0
antialias and normalize square wave FFT cos
0 cos = 0, sin = 0
1 cos = 1.2568, sin = 0
2 cos = 0, sin = 0
3 cos = -0.37415, sin = 0
4 cos = 0, sin = 0
5 cos = 0.16704, sin = 0
6 cos = 0, sin = 0
7 cos = -0.049728, sin = 0
 
 
square wave inverse FFT
0 real = 1, imag = 0
1 real = 1, imag = 0
2 real = 1, imag = 0
3 real = 1, imag = 0
4 real = 0, imag = 0
5 real = -1, imag = 0
6 real = -1, imag = 0
7 real = -1, imag = 0
8 real = -1, imag = 0
9 real = -1, imag = 0
10 real = -1, imag = 0
11 real = -1, imag = 0
12 real = 0, imag = 0
13 real = 1, imag = 0
14 real = 1, imag = 0
15 real = 1, imag = 0
 
 
square wave data, sin series
0 real = 0, imag = 0
1 real = 1, imag = 0
2 real = 1, imag = 0
3 real = 1, imag = 0
4 real = 1, imag = 0
5 real = 1, imag = 0
6 real = 1, imag = 0
7 real = 1, imag = 0
8 real = 0, imag = 0
9 real = -1, imag = 0
10 real = -1, imag = 0
11 real = -1, imag = 0
12 real = -1, imag = 0
13 real = -1, imag = 0
14 real = -1, imag = 0
15 real = -1, imag = 0
square wave generate, using sin
0 real = 0
1 real = 0.92884
2 real = 0.99731
3 real = 1.0263
4 real = 1.0353
5 real = 1.0263
6 real = 0.99731
7 real = 0.92884
8 real = 1.5021e-015
9 real = -0.92884
10 real = -0.99731
11 real = -1.0263
12 real = -1.0353
13 real = -1.0263
14 real = -0.99731
15 real = -0.92884
0 real = 0, imag = 0
1 real = 1, imag = 0
2 real = 1, imag = 0
3 real = 1, imag = 0
4 real = 1, imag = 0
5 real = 1, imag = 0
6 real = 1, imag = 0
7 real = 1, imag = 0
8 real = 0, imag = 0
9 real = -1, imag = 0
10 real = -1, imag = 0
11 real = -1, imag = 0
12 real = -1, imag = 0
13 real = -1, imag = 0
14 real = -1, imag = 0
15 real = -1, imag = 0
square wave FFT sin series
0 cos = 0, sin = 0
1 cos = 0, sin = -10.0547
2 cos = 0, sin = 0
3 cos = 0, sin = -2.9932
4 cos = 0, sin = 0
5 cos = 0, sin = -1.3364
6 cos = 0, sin = 0
7 cos = 0, sin = -0.39782
8 cos = 0, sin = 0
9 cos = 0, sin = 0.39782
10 cos = 0, sin = 0
11 cos = 0, sin = 1.3364
12 cos = 0, sin = 0
13 cos = 0, sin = 2.9932
14 cos = 0, sin = 0
15 cos = 0, sin = 10.0547
antialias and normalize square wave FFT sin
0 cos = 0, sin = 0
1 cos = 0, sin = 1.2568
2 cos = 0, sin = 0
3 cos = 0, sin = 0.37415
4 cos = 0, sin = 0
5 cos = 0, sin = 0.16704
6 cos = 0, sin = 0
7 cos = 0, sin = 0.049728
 
 
square wave data, sin no zeros
0 real = 1, imag = 0
1 real = 1, imag = 0
2 real = 1, imag = 0
3 real = 1, imag = 0
4 real = 1, imag = 0
5 real = 1, imag = 0
6 real = 1, imag = 0
7 real = 1, imag = 0
8 real = -1, imag = 0
9 real = -1, imag = 0
10 real = -1, imag = 0
11 real = -1, imag = 0
12 real = -1, imag = 0
13 real = -1, imag = 0
14 real = -1, imag = 0
15 real = -1, imag = 0
square wave FFT sin no zeros
0 cos = 0, sin = 0
1 cos = 2, sin = -10.0547
2 cos = 0, sin = 0
3 cos = 2, sin = -2.9932
4 cos = 0, sin = 0
5 cos = 2, sin = -1.3364
6 cos = 0, sin = 0
7 cos = 2, sin = -0.39782
8 cos = 0, sin = 0
9 cos = 2, sin = 0.39782
10 cos = 0, sin = 0
11 cos = 2, sin = 1.3364
12 cos = 0, sin = 0
13 cos = 2, sin = 2.9932
14 cos = 0, sin = 0
15 cos = 2, sin = 10.0547
antialias and normalize square wave FFT sin
0 cos = 0, sin = 0
1 cos = 0.25, sin = 1.2568
2 cos = 0, sin = 0
3 cos = 0.25, sin = 0.37415
4 cos = 0, sin = 0
5 cos = 0.25, sin = 0.16704
6 cos = 0, sin = 0
7 cos = 0.25, sin = 0.049728