4c82a578-6a63-41fb-ac07-9601fe834b17 13 6 5 auto

&[DATE] &[TIME] - &[FILENAME]

Sanity check Mathematica 4.0

Fourier complex  from sampled  Y vector [Numeric] Y fft N Y length : n 0 N range D n 1 + el 1 N sqrt / Y k 1 + el e i 2 π * n * N / (* k *^* (k 0 N 1 - sum * : for D 31 line :

Fourier "ifft" from complex sampled vector [Numeric] v ifft N v length 1 - : n 0 N 1 - range I n 1 + el 1 N sqrt / v k 1 + el e i 2 π * n * N / (* k * -^* (k 0 N 1 - sum * : for I 31 line :

Y 1.3 2.4 1.7 4.1 2.9 1.7 5.1 2.7 18 mat transpose :

Symbolic F Y fft :

Fraction => Auto F 7.742819 7.742819 - 21 sys 0.740685 - 0.677082 i * - 0.740685 0.677082 i * + 21 sys 0.919239 - 0.954594 i * - 0.919239 0.954594 i * + 21 sys 0.390685 - 1.727082 i * + 0.390685 1.727082 i * - 21 sys 0.035355 0.035355 - 21 sys 0.390685 - 1.727082 i * - 0.390685 1.727082 i * + 21 sys 0.919239 - 0.954594 i * + 0.919239 0.954594 i * - 21 sys 0.740685 - 0.677082 i * + 0.740685 0.677082 i * - 21 sys 7.742819 7.742819 - 21 sys 91 mat

v 7.742819 0.740685 - 0.677082 i * - 0.919239 - 0.954594 i * - 0.390685 - 1.727082 i * + 0.035355 0.390685 - 1.727082 i * - 0.919239 - 0.954594 i * + 0.740685 - 0.677082 i * + 7.742819 91 mat :

=> copy/paste =>

Symbolic sanity v ifft :

Fraction Auto sanity transpose 1310 / 1310 / - 21 sys 125 / 125 / - 21 sys 1710 / 1710 / - 21 sys 4110 / 4110 / - 21 sys 2910 / 2910 / - 21 sys 1710 / 1710 / - 21 sys 5110 / 5110 / - 21 sys 2710 / 2710 / - 21 sys 18 mat

1310 / 125 / 1710 / 4110 / 2910 / 1710 / 5110 / 2710 / 18 mat 1.3 2.4 1.7 4.1 2.9 1.7 5.1 2.7 18 mat ≡

Y 1 - 1 - 1 - 1 - 111118 mat transpose :

F Y fft :

F 0 0.707107 - 1.707107 i * - 0.707107 1.707107 i * + 21 sys 0021 sys 0.707107 - 0.292893 i * - 0.707107 0.292893 i * + 21 sys 0021 sys 0.707107 - 0.292893 i * + 0.707107 0.292893 i * - 21 sys 0021 sys 0.707107 - 1.707107 i * + 0.707107 1.707107 i * - 21 sys 0021 sys 91 mat

yy 0 0.707107 - 1.707107 i * - 0 0.707107 - 0.292893 i * - 0 0.707107 - 0.292893 i * + 0 0.707107 - 1.707107 i * + 091 mat :

=> copy/paste =>

Symbolic sanity yy ifft :

Fraction Auto sanity transpose 1 - 121 sys 1 - 121 sys 1 - 121 sys 1 - 121 sys 11 - 21 sys 11 - 21 sys 11 - 21 sys 11 - 21 sys 18 mat

Y 11 - 113 mat transpose :

Symbolic F Y fft :

Fraction => Auto F 0.57735 0.57735 - 21 sys 0.57735 i - 0.57735 - i + 21 sys 0.57735 i + 0.57735 - i - 21 sys 0.57735 0.57735 - 21 sys 41 mat

q 0.57735 0.57735 i - 0.57735 i + 0.57735 41 mat :

Symbolic sanity q ifft :

=> copy/paste =>

Fraction Auto sanity transpose 11 - 21 sys 1 - 121 sys 11 - 21 sys 13 mat