test_fft_big.c test fftd.c 
sin 2 th data 
[0] real = 0, imag = 0 
[1] real = 0.00613588, imag = 0 
[2] real = 0.0122715, imag = 0 
[3] real = 0.0184067, imag = 0 
[4] real = 0.0245412, imag = 0 
[5] real = 0.0306748, imag = 0 
[6] real = 0.0368072, imag = 0 
[7] real = 0.0429383, imag = 0 
[8] real = 0.0490677, imag = 0 
[9] real = 0.0551952, imag = 0 
[10] real = 0.0613207, imag = 0 
[11] real = 0.0674439, imag = 0 
[12] real = 0.0735646, imag = 0 
[13] real = 0.0796824, imag = 0 
[14] real = 0.0857973, imag = 0 
[15] real = 0.091909, imag = 0 
sin 2 th FFT 
cos 0 th = -1.53317e-15, sin 0 th = 0 
cos 1 th = 9.55343e-16, sin 1 th = 5.35409e-14 
cos 2 th = -1.39813e-11, sin 2 th = -1024 
cos 3 th = 3.39096e-15, sin 3 th = -9.54452e-14 
cos 4 th = 3.29793e-15, sin 4 th = -5.26283e-14 
cos 5 th = 5.84039e-15, sin 5 th = -3.61587e-14 
cos 6 th = -3.91378e-14, sin 6 th = -3.04112e-13 
cos 7 th = -6.13616e-15, sin 7 th = -2.19302e-14 
cos 8 th = 1.34873e-15, sin 8 th = -2.87379e-14 
cos 9 th = 8.33443e-15, sin 9 th = -1.37496e-14 
cos 10 th = 1.00066e-13, sin 10 th = -6.60099e-13 
cos 11 th = -1.12817e-14, sin 11 th = -1.11951e-14 
cos 12 th = -3.31243e-15, sin 12 th = -1.26979e-14 
cos 13 th = -2.61136e-15, sin 13 th = -1.56407e-14 
cos 14 th = -2.22833e-14, sin 14 th = -8.54601e-14 
cos 15 th = 1.10773e-15, sin 15 th = -1.58281e-14 
antialias and normalize sin 2 th FFT 
cos 0 th = -7.48618e-19, sin 0 th = -0 
cos 1 th = 9.32953e-19, sin 1 th = -5.22861e-17 
cos 2 th = -6.11219e-15, sin 2 th = 1 
cos 3 th = 3.31148e-18, sin 3 th = 9.32082e-17 
cos 4 th = 3.22064e-18, sin 4 th = 5.13948e-17 
cos 5 th = 5.7035e-18, sin 5 th = 3.53112e-17 
cos 6 th = -5.88326e-17, sin 6 th = 2.97459e-16 
cos 7 th = -5.99234e-18, sin 7 th = 2.14162e-17 
cos 8 th = 1.31712e-18, sin 8 th = 2.80643e-17 


cos 2 th data 
[0] real = 1, imag = 0 
[1] real = 0.999981, imag = 0 
[2] real = 0.999925, imag = 0 
[3] real = 0.999831, imag = 0 
[4] real = 0.999699, imag = 0 
[5] real = 0.999529, imag = 0 
[6] real = 0.999322, imag = 0 
[7] real = 0.999078, imag = 0 
[8] real = 0.998795, imag = 0 
[9] real = 0.998476, imag = 0 
[10] real = 0.998118, imag = 0 
[11] real = 0.997723, imag = 0 
[12] real = 0.99729, imag = 0 
[13] real = 0.99682, imag = 0 
[14] real = 0.996313, imag = 0 
[15] real = 0.995767, imag = 0 
cos 2 th FFT 
cos 0 th = -7.4753e-14, sin 0 th = 0 
cos 1 th = -1.08163e-13, sin 1 th = 2.96961e-15 
cos 2 th = 1024, sin 2 th = -1.397e-11 
cos 3 th = 6.39297e-14, sin 3 th = -1.50443e-15 
cos 4 th = 2.33943e-14, sin 4 th = 1.38723e-15 
cos 5 th = 2.04955e-14, sin 5 th = -8.34799e-15 
cos 6 th = 8.65251e-13, sin 6 th = 5.55059e-14 
cos 7 th = 1.01182e-14, sin 7 th = 7.09753e-15 
cos 8 th = 4.27767e-15, sin 8 th = 6.56162e-15 
cos 9 th = 1.65529e-15, sin 9 th = 5.77754e-15 
cos 10 th = 1.02761e-12, sin 10 th = 1.14319e-13 
cos 11 th = -2.0401e-15, sin 11 th = -6.36152e-15 
cos 12 th = 1.08554e-14, sin 12 th = 9.47703e-16 
cos 13 th = -3.36927e-15, sin 13 th = 4.00956e-15 
cos 14 th = 3.07833e-13, sin 14 th = 2.60302e-14 
cos 15 th = -4.9251e-15, sin 15 th = -3.99294e-15 
antialias and normalize cos 2 th FFT 
cos 0 th = -3.65005e-17, sin 0 th = -0 
cos 1 th = -1.05628e-16, sin 1 th = -2.90001e-18 
cos 2 th = 1, sin 2 th = 6.11313e-15 
cos 3 th = 6.24313e-17, sin 3 th = 1.46917e-18 
cos 4 th = 2.2846e-17, sin 4 th = -1.35471e-18 
cos 5 th = 2.00151e-17, sin 5 th = 8.15233e-18 
cos 6 th = -2.55018e-16, sin 6 th = -7.02895e-17 
cos 7 th = 9.88107e-18, sin 7 th = -6.93119e-18 
cos 8 th = 4.17741e-18, sin 8 th = -6.40783e-18 


1.0 + cos 2 th data 
[0] real = 2, imag = 0 
[1] real = 1.99998, imag = 0 
[2] real = 1.99992, imag = 0 
[3] real = 1.99983, imag = 0 
[4] real = 1.9997, imag = 0 
[5] real = 1.99953, imag = 0 
[6] real = 1.99932, imag = 0 
[7] real = 1.99908, imag = 0 
[8] real = 1.9988, imag = 0 
[9] real = 1.99848, imag = 0 
[10] real = 1.99812, imag = 0 
[11] real = 1.99772, imag = 0 
[12] real = 1.99729, imag = 0 
[13] real = 1.99682, imag = 0 
[14] real = 1.99631, imag = 0 
[15] real = 1.99577, imag = 0 
cos 2 th FFT 
cos 0 th = 2048, sin 0 th = 0 
cos 1 th = -1.08097e-13, sin 1 th = 2.64023e-15 
cos 2 th = 1024, sin 2 th = -1.39637e-11 
cos 3 th = 6.27195e-14, sin 3 th = 6.87359e-16 
cos 4 th = 3.15886e-14, sin 4 th = 6.11876e-15 
cos 5 th = 1.9414e-14, sin 5 th = -6.15051e-15 
cos 6 th = 8.66089e-13, sin 6 th = 5.24145e-14 
cos 7 th = 1.16279e-14, sin 7 th = 1.15411e-14 
cos 8 th = -4.63645e-15, sin 8 th = -7.79563e-15 
cos 9 th = 3.7735e-15, sin 9 th = 9.41147e-15 
cos 10 th = 1.03329e-12, sin 10 th = 1.21859e-13 
cos 11 th = 8.49582e-16, sin 11 th = -2.31673e-15 
cos 12 th = 1.03845e-14, sin 12 th = 3.94659e-15 
cos 13 th = -2.95118e-15, sin 13 th = 5.24984e-15 
cos 14 th = 3.02367e-13, sin 14 th = 2.61967e-14 
cos 15 th = -3.36911e-15, sin 15 th = -6.42129e-15 
antialias and normalize 1.0 + cos 2 th FFT 
cos 0 th = 1, sin 0 th = -0 
cos 1 th = -1.05564e-16, sin 1 th = -2.57835e-18 
cos 2 th = 1, sin 2 th = 6.10481e-15 
cos 3 th = 6.12495e-17, sin 3 th = -6.71249e-19 
cos 4 th = 3.08483e-17, sin 4 th = -5.97535e-18 
cos 5 th = 1.8959e-17, sin 5 th = 6.00635e-18 
cos 6 th = -2.51198e-16, sin 6 th = -6.61356e-17 
cos 7 th = 1.13553e-17, sin 7 th = -1.12706e-17 
cos 8 th = -4.52778e-18, sin 8 th = 7.61292e-18 


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 = 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 generate, using cos 
[0] real = 1.03526 
[1] real = 1.03521 
[2] real = 1.03504 
[3] real = 1.03478 
[4] real = 1.0344 
[5] real = 1.03392 
[6] real = 1.03334 
[7] real = 1.03265 
[8] real = 1.03186 
[9] real = 1.03098 
[10] real = 1.03 
[11] real = 1.02893 
[12] real = 1.02777 
[13] real = 1.02653 
[14] real = 1.0252 
[15] real = 1.0238 
square wave FFT cos series 
cos 0 th = 0, sin 0 th = 0 
cos 1 th = 1303.8, sin 1 th = -1.96975e-11 
cos 2 th = 0, sin 2 th = 0 
cos 3 th = -434.596, sin 3 th = 5.94779e-12 
cos 4 th = 0, sin 4 th = 0 
cos 5 th = 260.754, sin 5 th = -3.61381e-12 
cos 6 th = 0, sin 6 th = 0 
cos 7 th = -186.25, sin 7 th = 2.23512e-12 
cos 8 th = 0, sin 8 th = 0 
cos 9 th = 144.857, sin 9 th = -1.84894e-12 
cos 10 th = 0, sin 10 th = 0 
cos 11 th = -118.516, sin 11 th = 1.4027e-12 
cos 12 th = 0, sin 12 th = 0 
cos 13 th = 100.279, sin 13 th = -1.22525e-12 
cos 14 th = 0, sin 14 th = 0 
cos 15 th = -86.9045, sin 15 th = 8.82466e-13 
antialias and normalize square wave FFT cos
cos 0 th = 0, sin 0 th = -0 
cos 1 th = 1.27324, sin 1 th = 8.5442e-15 
cos 2 th = 0, sin 2 th = -0 
cos 3 th = -0.42441, sin 3 th = -2.20234e-15 
cos 4 th = 0, sin 4 th = -0 
cos 5 th = 0.254643, sin 5 th = 1.3859e-15 
cos 6 th = 0, sin 6 th = -0 
cos 7 th = -0.181884, sin 7 th = -7.3225e-16 
cos 8 th = 0, sin 8 th = -0 
square wave inverse FFT 
rdat 0 = 1 
rdat 1 = 1 
rdat 2 = 1 
rdat 3 = 1 
rdat 4 = 1 
rdat 5 = 1 
rdat 6 = 1 
rdat 7 = 1 
rdat 8 = 1 
rdat 9 = 1 
rdat 10 = 1 
rdat 11 = 1 
rdat 12 = 1 
rdat 13 = 1 
rdat 14 = 1 
rdat 15 = 1 


square wave data, for 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 = 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 generate, using sin 
[0] real = 0 
[1] real = 0.0351503 
[2] real = 0.070265 
[3] real = 0.105309 
[4] real = 0.140246 
[5] real = 0.175041 
[6] real = 0.209659 
[7] real = 0.244066 
[8] real = 0.278227 
[9] real = 0.312109 
[10] real = 0.345678 
[11] real = 0.378902 
[12] real = 0.411748 
[13] real = 0.444184 
[14] real = 0.476181 
[15] real = 0.507708 
square wave FFT sin series 
cos 0 th = 0, sin 0 th = 0 
cos 1 th = -1.97835e-11, sin 1 th = -1303.8 
cos 2 th = 0, sin 2 th = 0 
cos 3 th = -5.84569e-12, sin 3 th = -434.596 
cos 4 th = 0, sin 4 th = 0 
cos 5 th = -3.58939e-12, sin 5 th = -260.754 
cos 6 th = 0, sin 6 th = 0 
cos 7 th = -2.25967e-12, sin 7 th = -186.25 
cos 8 th = 0, sin 8 th = 0 
cos 9 th = -1.88343e-12, sin 9 th = -144.857 
cos 10 th = 0, sin 10 th = 0 
cos 11 th = -1.39743e-12, sin 11 th = -118.516 
cos 12 th = 0, sin 12 th = 0 
cos 13 th = -1.20212e-12, sin 13 th = -100.279 
cos 14 th = 0, sin 14 th = 0 
cos 15 th = -9.50045e-13, sin 15 th = -86.9045 
antialias and normalize square wave FFT sin
cos 0 th = 0, sin 0 th = -0 
cos 1 th = -8.61973e-15, sin 1 th = 1.27324 
cos 2 th = 0, sin 2 th = -0 
cos 3 th = -2.14691e-15, sin 3 th = 0.42441 
cos 4 th = 0, sin 4 th = -0 
cos 5 th = -1.38469e-15, sin 5 th = 0.254643 
cos 6 th = 0, sin 6 th = -0 
cos 7 th = -7.45478e-16, sin 7 th = 0.181884 
cos 8 th = 0, sin 8 th = -0 
square wave inverse FFT 
rdat 0 = 0 
rdat 1 = 1 
rdat 2 = 1 
rdat 3 = 1 
rdat 4 = 1 
rdat 5 = 1 
rdat 6 = 1 
rdat 7 = 1 
rdat 8 = 1 
rdat 9 = 1 
rdat 10 = 1 
rdat 11 = 1 
rdat 12 = 1 
rdat 13 = 1 
rdat 14 = 1 
rdat 15 = 1 


square wave data, for sin, no zero 
          note: cos values come in 
[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 series, no zero 
cos 0 th = 0, sin 0 th = 0 
cos 1 th = 2, sin 1 th = -1303.8 
cos 2 th = 0, sin 2 th = 0 
cos 3 th = 2, sin 3 th = -434.596 
cos 4 th = 0, sin 4 th = 0 
cos 5 th = 2, sin 5 th = -260.754 
cos 6 th = 0, sin 6 th = 0 
cos 7 th = 2, sin 7 th = -186.25 
cos 8 th = 0, sin 8 th = 0 
cos 9 th = 2, sin 9 th = -144.857 
cos 10 th = 0, sin 10 th = 0 
cos 11 th = 2, sin 11 th = -118.516 
cos 12 th = 0, sin 12 th = 0 
cos 13 th = 2, sin 13 th = -100.279 
cos 14 th = 0, sin 14 th = 0 
cos 15 th = 2, sin 15 th = -86.9045 
antialias and normalize square wave FFT sin, no zero
cos 0 th = 0, sin 0 th = -0 
cos 1 th = 0.00195312, sin 1 th = 1.27324 
cos 2 th = 0, sin 2 th = -0 
cos 3 th = 0.00195312, sin 3 th = 0.42441 
cos 4 th = 0, sin 4 th = -0 
cos 5 th = 0.00195312, sin 5 th = 0.254643 
cos 6 th = 0, sin 6 th = -0 
cos 7 th = 0.00195312, sin 7 th = 0.181884 
cos 8 th = 0, sin 8 th = -0 
square wave inverse FFT, sin, no zero 
rdat 0 = 1 
rdat 1 = 1 
rdat 2 = 1 
rdat 3 = 1 
rdat 4 = 1 
rdat 5 = 1 
rdat 6 = 1 
rdat 7 = 1 
rdat 8 = 1 
rdat 9 = 1 
rdat 10 = 1 
rdat 11 = 1 
rdat 12 = 1 
rdat 13 = 1 
rdat 14 = 1 
rdat 15 = 1 


triangle wave data, cos series 
[0] real = 1, imag = 0 
[1] real = 0.998047, imag = 0 
[2] real = 0.996094, imag = 0 
[3] real = 0.994141, imag = 0 
[4] real = 0.992188, imag = 0 
[5] real = 0.990234, imag = 0 
[6] real = 0.988281, imag = 0 
[7] real = 0.986328, imag = 0 
[8] real = 0.984375, imag = 0 
[9] real = 0.982422, imag = 0 
[10] real = 0.980469, imag = 0 
[11] real = 0.978516, imag = 0 
[12] real = 0.976562, imag = 0 
[13] real = 0.974609, imag = 0 
[14] real = 0.972656, imag = 0 
[15] real = 0.970703, imag = 0 
triangle wave generate, cos series 
[0] real = 0.977507 
[1] real = 0.977473 
[2] real = 0.97737 
[3] real = 0.977198 
[4] real = 0.976959 
[5] real = 0.976651 
[6] real = 0.976275 
[7] real = 0.975832 
[8] real = 0.975322 
[9] real = 0.974745 
[10] real = 0.974103 
[11] real = 0.973395 
[12] real = 0.972623 
[13] real = 0.971787 
[14] real = 0.970888 
[15] real = 0.969927 
triangle wave FFT 
cos 0 th = 0, sin 0 th = 0 
cos 1 th = 830.024, sin 1 th = -1.2467e-11 
cos 2 th = 0, sin 2 th = 0 
cos 3 th = 92.2254, sin 3 th = -1.22739e-12 
cos 4 th = 0, sin 4 th = 0 
cos 5 th = 33.2016, sin 5 th = -4.36595e-13 
cos 6 th = 0, sin 6 th = 0 
cos 7 th = 16.9399, sin 7 th = -1.75707e-13 
cos 8 th = 0, sin 8 th = 0 
cos 9 th = 10.2479, sin 9 th = -2.43871e-14 
cos 10 th = 0, sin 10 th = 0 
cos 11 th = 6.86035, sin 11 th = -6.62037e-14 
cos 12 th = 0, sin 12 th = 0 
cos 13 th = 4.91203, sin 13 th = -4.58322e-14 
cos 14 th = 0, sin 14 th = 0 
cos 15 th = 3.68964, sin 15 th = -1.12248e-14 
antialias and normalize triangular wave FFT cos
cos 0 th = 0, sin 0 th = -0 
cos 1 th = 0.81057, sin 1 th = 5.41967e-15 
cos 2 th = 0, sin 2 th = -0 
cos 3 th = 0.0900639, sin 3 th = 4.52859e-16 
cos 4 th = 0, sin 4 th = -0 
cos 5 th = 0.0324234, sin 5 th = 1.58871e-16 
cos 6 th = 0, sin 6 th = -0 
cos 7 th = 0.0165429, sin 7 th = 2.15256e-18 
cos 8 th = 0, sin 8 th = -0 


triangle wave data, sin series 
[0] real = 0, imag = 0 
[1] real = 0.00195312, imag = 0 
[2] real = 0.00390625, imag = 0 
[3] real = 0.00585938, imag = 0 
[4] real = 0.0078125, imag = 0 
[5] real = 0.00976562, imag = 0 
[6] real = 0.0117188, imag = 0 
[7] real = 0.0136719, imag = 0 
[8] real = 0.015625, imag = 0 
[9] real = 0.0175781, imag = 0 
[10] real = 0.0195312, imag = 0 
[11] real = 0.0214844, imag = 0 
[12] real = 0.0234375, imag = 0 
[13] real = 0.0253906, imag = 0 
[14] real = 0.0273438, imag = 0 
[15] real = 0.0292969, imag = 0 
triangle wave generate, sin series 
[0] real = 0 
[1] real = 0.00202196 
[2] real = 0.0040437 
[3] real = 0.00606503 
[4] real = 0.00808573 
[5] real = 0.0101056 
[6] real = 0.0121244 
[7] real = 0.014142 
[8] real = 0.0161581 
[9] real = 0.0181726 
[10] real = 0.0201853 
[11] real = 0.022196 
[12] real = 0.0242045 
[13] real = 0.0262107 
[14] real = 0.0282144 
[15] real = 0.0302154 
triangle wave FFT 
cos 0 th = 0, sin 0 th = 0 
cos 1 th = -1.24779e-11, sin 1 th = -830.024 
cos 2 th = 0, sin 2 th = 0 
cos 3 th = 1.22994e-12, sin 3 th = 92.2254 
cos 4 th = 0, sin 4 th = 0 
cos 5 th = -4.39649e-13, sin 5 th = -33.2016 
cos 6 th = 0, sin 6 th = 0 
cos 7 th = 1.83787e-13, sin 7 th = 16.9399 
cos 8 th = 0, sin 8 th = 0 
cos 9 th = -2.93471e-14, sin 9 th = -10.2479 
cos 10 th = 0, sin 10 th = 0 
cos 11 th = 7.00899e-14, sin 11 th = 6.86035 
cos 12 th = 0, sin 12 th = 0 
cos 13 th = -4.8124e-14, sin 13 th = -4.91203 
cos 14 th = 0, sin 14 th = 0 
cos 15 th = 3.51821e-14, sin 15 th = 3.68964 
antialias and normalize triangular wave FFT sin
cos 0 th = 0, sin 0 th = -0 
cos 1 th = -5.4243e-15, sin 1 th = 0.81057 
cos 2 th = 0, sin 2 th = -0 
cos 3 th = 4.52733e-16, sin 3 th = -0.0900639 
cos 4 th = 0, sin 4 th = -0 
cos 5 th = -1.58401e-16, sin 5 th = 0.0324234 
cos 6 th = 0, sin 6 th = -0 
cos 7 th = 4.48912e-18, sin 7 th = -0.0165429 
cos 8 th = 0, sin 8 th = -0 


saw tooth wave data, sin series 
[0] real = 0, imag = 0 
[1] real = 0.000976562, imag = 0 
[2] real = 0.00195312, imag = 0 
[3] real = 0.00292969, imag = 0 
[4] real = 0.00390625, imag = 0 
[5] real = 0.00488281, imag = 0 
[6] real = 0.00585938, imag = 0 
[7] real = 0.00683594, imag = 0 
[8] real = 0.0078125, imag = 0 
[9] real = 0.00878906, imag = 0 
[10] real = 0.00976562, imag = 0 
[11] real = 0.0107422, imag = 0 
[12] real = 0.0117188, imag = 0 
[13] real = 0.0126953, imag = 0 
[14] real = 0.0136719, imag = 0 
[15] real = 0.0146484, imag = 0 
sawtooth wave generate 
[0] real = 0 
[1] real = 9.64947e-07 
[2] real = 7.71501e-06 
[3] real = 2.60125e-05 
[4] real = 6.15742e-05 
[5] real = 0.000120049 
[6] real = 0.000206995 
[7] real = 0.000327858 
[8] real = 0.000487951 
[9] real = 0.000692432 
[10] real = 0.000946283 
[11] real = 0.00125429 
[12] real = 0.00162103 
[13] real = 0.00205085 
[14] real = 0.00254784 
[15] real = 0.00311583 
saw tooth wave FFT, sin series 
cos 0 th = 0, sin 0 th = 0 
cos 1 th = -9.89175e-12, sin 1 th = -651.898 
cos 2 th = 4.41536e-12, sin 2 th = 325.948 
cos 3 th = -2.92285e-12, sin 3 th = -217.298 
cos 4 th = 1.96651e-12, sin 4 th = 162.973 
cos 5 th = -1.79469e-12, sin 5 th = -130.377 
cos 6 th = 1.32841e-12, sin 6 th = 108.647 
cos 7 th = -1.12983e-12, sin 7 th = -93.1248 
cos 8 th = 8.41653e-13, sin 8 th = 81.4832 
cos 9 th = -9.41713e-13, sin 9 th = -72.4286 
cos 10 th = 7.67217e-13, sin 10 th = 65.1848 
cos 11 th = -6.98714e-13, sin 11 th = -59.2579 
cos 12 th = 5.59559e-13, sin 12 th = 54.3188 
cos 13 th = -6.01061e-13, sin 13 th = -50.1394 
cos 14 th = 4.75706e-13, sin 14 th = 46.557 
cos 15 th = -4.75022e-13, sin 15 th = -43.4522 
antialias and normalize saw tooth wave FFT sin
cos 0 th = 0, sin 0 th = -0 
cos 1 th = -4.30986e-15, sin 1 th = 0.636619 
cos 2 th = 1.89303e-15, sin 2 th = -0.318309 
cos 3 th = -1.07346e-15, sin 3 th = 0.212205 
cos 4 th = 8.36686e-16, sin 4 th = -0.159153 
cos 5 th = -6.92346e-16, sin 5 th = 0.127321 
cos 6 th = 4.99588e-16, sin 6 th = -0.1061 
cos 7 th = -3.72739e-16, sin 7 th = 0.0909422 
cos 8 th = 3.60067e-16, sin 8 th = -0.0795735 

cos 1023 th = 1.3642e-16, sin 1023 th = -0.00153398 
cos 1024 th = 0, sin 1024 th = 0 
cos 1025 th = 1.0531e-12, sin 1025 th = 0.00153398