If I get up the energy to play with this stuff, I can probably put together a rough 'FFT' based summer (that is, not an FFT, but power based) to see what forcing the phases to match would sound like.  I suspect the results would at least be grainy sounding (like some of the ABBA recordings due to the abuse of the quadrature/destroying the analytical nature of the signal), but more than likely renders the sound unintelligible.

Actually, I have done something similar before -- by zeroing the phase of a given FFT (magnitudes the same, phase is zeroed -- all the same), and the result was pretty much unintelligble-- it was possible to detect some of the material, but didn't seem to be useful.

The comment about a true FFT being a linear transform is true -- add an FFT (each) of two signals and the result will be the same as an FFT of the sum of the actual time domain originals.

Quote from: jsdyson on 2018-04-23 18:23:09

The comment about a true FFT being a linear transform is true -- add an FFT (each) of two signals and the result will be the same as an FFT of the sum of the actual time domain originals.

WHAAAAAT?
Let's assume we have a signal and an inverse of it. If we FFT both, we get same freqs and amps, but another phases (which doesn't matter while listening). However if we sum anticorrelated signals, we get NOTHING. LITERALLY NOTHING. FFT OF NOTHING IS NOTHING.
How can be average of FFTs of something be equal to FFT of nothing?

Quote from: jsdyson on 2018-04-23 18:23:09

The comment about a true FFT being a linear transform is true -- add an FFT (each) of two signals and the result will be the same as an FFT of the sum of the actual time domain originals.

WHAAAAAT?

How can be average of FFTs of something be equal to FFT of nothing?

OK... but how does it happen?

FFT of zero: FREQ 0, AMPL 0, PHASE 0.

Average of FFTs: FREQ freq, AMPL ampl, PHASE (phase1 + phase2) / 2

So if I FFT'd both channels of the signal, averaged coefficients and IFFT'd them, would it do the same as simply averaging both signals?

Quote from: jsdyson on 2018-04-23 18:23:09

If I get up the energy to play with this stuff, I can probably put together a rough 'FFT' based summer (that is, not an FFT, but power based) to see what forcing the phases to match would sound like.  I suspect the results would at least be grainy sounding (like some of the ABBA recordings due to the abuse of the quadrature/destroying the analytical nature of the signal), but more than likely renders the sound unintelligible.

Actually, I have done something similar before -- by zeroing the phase of a given FFT (magnitudes the same, phase is zeroed -- all the same), and the result was pretty much unintelligble-- it was possible to detect some of the material, but didn't seem to be useful.

Can you send us some samples, please? And why does it happen?

I believe @ziemek.z misunderstanding of FFT (i.e. the fact that FFT returns a complex function from a real variable) comes from how audio editors often display FFTs. Many - including Audacity - display it as a sequence of buckets, where frequencies of each bucket are painted in a voiceprint. The tools often quitely ignore the Imaginary part of the resulting function, and simply paint the magnitude of the complex value, and ignore the argument, which in that case is phase.

Quote from: polemon on 2018-04-24 00:59:32

I believe @ziemek.z misunderstanding of FFT (i.e. the fact that FFT returns a complex function from a real variable) comes from how audio editors often display FFTs. Many - including Audacity - display it as a sequence of buckets, where frequencies of each bucket are painted in a voiceprint. The tools often quitely ignore the Imaginary part of the resulting function, and simply paint the magnitude of the complex value, and ignore the argument, which in that case is phase.

Okay -- that makes sense.  From what I know (and from my previous practical experience), the phase is all important.  When I wrote my prototype compressor/expander, the math operations were done on complex numbers.  Using magnitudes only was just a waste of time and just produced garbage.

Quote from: jsdyson on 2018-04-24 01:18:20

Quote from: polemon on 2018-04-24 00:59:32

I believe @ziemek.z misunderstanding of FFT (i.e. the fact that FFT returns a complex function from a real variable) comes from how audio editors often display FFTs. Many - including Audacity - display it as a sequence of buckets, where frequencies of each bucket are painted in a voiceprint. The tools often quitely ignore the Imaginary part of the resulting function, and simply paint the magnitude of the complex value, and ignore the argument, which in that case is phase.

Okay -- that makes sense.  From what I know (and from my previous practical experience), the phase is all important.  When I wrote my prototype compressor/expander, the math operations were done on complex numbers.  Using magnitudes only was just a waste of time and just produced garbage.

Depends. If you have a signal that is even (symmetric at center) in your bucket, the Imaginary part of your FFT of that signal is zero. The magnitude is then only the Real part.
In cases where a voiceprint is displayed (I'm not sure "voiceprint" is the correct term, I've seen it a bunch of times, though), it seems it's /just/ being used for display purposes, mixing anything even when using that display option, doesn't mean the actual FFT of that signal is used, and it seems indeed it almost never (in my experience) is.

If your sample bucket is small enough such that it is manageable, you can move all samples beyond the center, map them into the negative part by duplicating them symmetrically, and then run the FFT on that. The Imaginary part of the signal in that bucket will be zero (or equal to the zero function rather). Using this for anything but display purposes isn't really sensical, though.