[Chabsff]

And phase. People always forget about the phase as if it was purely imaginary.

[JKCalhoun]

Ha ha, as I understand it, phase is imaginary in a Fourier transform. Complex numbers are used and the imaginary portion does indeed represent phase.

I have been told that reversing the process — creating a time-based waveform — will not resemble (visually) the original due to this phase loss in the round-tripping. But then our brain never paid phase any mind so it will sound the same to our ears. (Yay, MP3!)

[xeonmc]

Actually, by the Kramers-Kronig relation you can infer the imaginary part just from the real parts, if given that your time signal is causal. So the phase isn’t actually lost in any way at all, if you assume causality.

Also, pedantic nit: phase would be the imaginary exponent of the spectrum rather than the imaginary part directly, i.e, you take the logarithm of the complex amplitude to get log-magnitude (real) plus phase (imag)

[Chabsff]

I'm glad someone picked up on my dumb joke :), I was getting worried.

That being said, round-tripping works just fine, axiomatically so, until you go out of your way to discard the imaginary component.