DFT < test.dat
# discrete Fourier transform
# Frequency real imaginary Power Spectrum Amplitude spectrum Phase spectrum
0 4.000000 0.000000 16.000000 1.000000 0.000000
1 1.000000 -2.414214 6.828427 0.653281 -1.178097
2 -0.000000 -0.000000 0.000000 0.000000 0.879647
3 1.000000 -0.414214 1.171573 0.270598 -0.392699
4 0.000000 -0.000000 0.000000 0.000000 0.000000
5 1.000000 0.414214 1.171573 0.270598 0.392699
6 0.000000 -0.000000 0.000000 0.000000 -0.791498
7 1.000000 2.414214 6.828427 0.653281 1.178097
# inverse discrete Fourier transform
# t real imaginary
0 1.000000 0.000000
1 1.000000 -0.000000
2 1.000000 -0.000000
3 1.000000 0.000000
4 -0.000000 -0.000000
5 -0.000000 0.000000
6 -0.000000 -0.000000
7 0.000000 0.000000