marcan
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Play original musical signal through 2 parametric filters that reverse each other: (1) +3 dB @ 4.5 kHz, Q=0.67, then (2) -3 dB @ 4.5 kHz, Q=0.67. If both EQs were perfect, the final waveform would be identical to the original.
It won't be check it. You will necessarily add noise in the time domain. If you use a linear phase you will have pre ringing which is particularly unnatural (in the real world you don't hear a sound before it starts). If you use a minimal phase you will have post ringing which is more natural (in the real world you always hear a tail after a sound) but the phase is compromised. Nowadays there is no way around it.
I'm willing to try this experiment. I can create 2 WAV files in exactly this way and post them here. Anyone can load them into a DBT app and see if they can tell them apart without guessing (confidence > 95%).
To be fair to your point, if we used a more extreme filter - bigger amplitude or steeper slope - then at some point the distortions you mention become audible. But not with slopes at 3 dB / octave.
Sure I'm ready to abx