h(t)=real-valued even-function h(n)=h(N-n) and real? n real(n) imag.(n) real(N-n) imag.(N-n) 0 25.127533 0.000000 25.127533 0.000000 1 -3.622967 0.000000 -3.622967 0.000000 2 -0.310545 0.000000 -0.310545 0.000000 3 -0.188846 0.000000 -0.188846 0.000000 4 -0.106400 0.000000 -0.106400 0.000000 5 -0.070291 0.000000 -0.070291 0.000000 6 -0.050611 0.000000 -0.050611 0.000000 7 -0.038820 0.000000 -0.038820 0.000000 8 -0.031248 0.000000 -0.031248 0.000000 9 -0.026148 0.000000 -0.026148 0.000000 10 -0.022600 0.000000 -0.022600 0.000000 11 -0.020089 0.000000 -0.020089 0.000000 12 -0.018306 0.000000 -0.018306 0.000000 13 -0.017063 0.000000 -0.017063 0.000000 14 -0.016243 0.000000 -0.016243 0.000000 15 -0.015776 0.000000 -0.015776 0.000000 16 -0.015625 0.000000 -0.015625 0.000000 press return to continue ... h(t)=imaginary-valued even-function h(n)=h(N-n) and imaginary? n real(n) imag.(n) real(N-n) imag.(N-n) 0 0.000000 25.127533 0.000000 25.127533 1 0.000000 -3.622967 0.000000 -3.622967 2 0.000000 -0.310545 0.000000 -0.310545 3 0.000000 -0.188846 0.000000 -0.188846 4 0.000000 -0.106400 0.000000 -0.106400 5 0.000000 -0.070291 0.000000 -0.070291 6 0.000000 -0.050611 0.000000 -0.050611 7 0.000000 -0.038820 0.000000 -0.038820 8 0.000000 -0.031248 0.000000 -0.031248 9 0.000000 -0.026148 0.000000 -0.026148 10 0.000000 -0.022600 0.000000 -0.022600 11 0.000000 -0.020089 0.000000 -0.020089 12 0.000000 -0.018306 0.000000 -0.018306 13 0.000000 -0.017063 0.000000 -0.017063 14 0.000000 -0.016243 0.000000 -0.016243 15 0.000000 -0.015776 0.000000 -0.015776 16 0.000000 -0.015625 0.000000 -0.015625 press return to continue ... h(t)=real-valued odd-function h(n) = -h(N-n) and imaginary? n real(n) imag.(n) real(N-n) imag.(N-n) 0 0.000000 0.000000 0.000000 0.000000 1 0.000000 -7.495315 0.000000 7.495315 2 0.000000 -2.473274 0.000000 2.473274 3 0.000000 -1.670007 0.000000 1.670007 4 0.000000 -1.214651 0.000000 1.214651 5 0.000000 -0.939447 0.000000 0.939447 6 0.000000 -0.750628 0.000000 0.750628 7 0.000000 -0.610711 0.000000 0.610711 8 0.000000 -0.500967 0.000000 0.500967 9 0.000000 -0.411005 0.000000 0.411005 10 0.000000 -0.334558 0.000000 0.334558 11 0.000000 -0.267589 0.000000 0.267589 12 0.000000 -0.207343 0.000000 0.207343 13 0.000000 -0.151834 0.000000 0.151834 14 0.000000 -0.099557 0.000000 0.099557 15 0.000000 -0.049294 0.000000 0.049294 16 0.000000 0.000000 0.000000 0.000000 press return to continue ... h(t)=imaginary-valued odd-function h(n) = -h(N-n) and real? n real(n) imag.(n) real(N-n) imag.(N-n) 0 0.000000 0.000000 0.000000 0.000000 1 7.495315 0.000000 -7.495315 0.000000 2 2.473274 0.000000 -2.473274 0.000000 3 1.670007 0.000000 -1.670007 0.000000 4 1.214651 0.000000 -1.214651 0.000000 5 0.939447 0.000000 -0.939447 0.000000 6 0.750628 0.000000 -0.750628 0.000000 7 0.610711 0.000000 -0.610711 0.000000 8 0.500967 0.000000 -0.500967 0.000000 9 0.411005 0.000000 -0.411005 0.000000 10 0.334558 0.000000 -0.334558 0.000000 11 0.267589 0.000000 -0.267589 0.000000 12 0.207343 0.000000 -0.207343 0.000000 13 0.151834 0.000000 -0.151834 0.000000 14 0.099557 0.000000 -0.099557 0.000000 15 0.049294 0.000000 -0.049294 0.000000 16 0.000000 0.000000 0.000000 0.000000 press return to continue ... original data: double fourier transform: k real h(k) imag h(k) real h(k) imag h(k) 1 0.800000 -0.194700 0.800000 -0.194700 2 0.819856 -0.188142 0.819856 -0.188142 3 0.839344 -0.180643 0.839344 -0.180643 4 0.858340 -0.172222 0.858340 -0.172222 5 0.876712 -0.162903 0.876712 -0.162903 6 0.894323 -0.152720 0.894323 -0.152720 7 0.911032 -0.141713 0.911032 -0.141713 8 0.926697 -0.129930 0.926697 -0.129930 9 0.941176 -0.117427 0.941176 -0.117427 10 0.954334 -0.104264 0.954334 -0.104264 11 0.966038 -0.090511 0.966038 -0.090511 12 0.976168 -0.076241 0.976168 -0.076241 13 0.984615 -0.061531 0.984615 -0.061531 14 0.991288 -0.046465 0.991288 -0.046465 15 0.996109 -0.031128 0.996109 -0.031128 16 0.999024 -0.015610 0.999024 -0.015610