Il 04/07/26 19:36, Robin Gareus ha scritto:
On 2026-07-04 1:04 PM, Fons Adriaensen wrote:
On a more philosophical note: almost all the math theory that
describes physical processes (e.g. differential equations)
requires complex numbers. In other words, numbers that combine
amplitude and phase into a single concept. There is in general
no reason to assume that any process would modify only one of
them and leave the other alone when not unnaturally contrived
to do so.
Except the human ear is does not perceive phase. Radio stations use[d]
all-pass filters to shift peaks so they could add more gain before
clipping. A few years ago I wrote a phase-rotate plugin [1] to
experiment with this. I found if fascinating to rotate the phase of a
square-wave, which results in vastly different waveform shapes without
my ear being able to hear any difference whatsoever.
I used to think that we don't perceive phase as well but, no, that's not
true. Two examples: 1. Feed a Moog-like filter with a sawtooth wave and
try again phase-inverting it. 2. Take a static waveform of your choice
with a limited number of predominant harmonics and then resynthesize it
keeping the magnitudes and randomizing the phases - most of the times
you won't perceive a difference but sometimes you'll do.
Anyway, dynamic range reduction through allpass filters was also studied
in [1] and [2].
Stefano D'Angelo
[1] J. Parker, V. Valimaki, "Linear Dynamic Range Reduction of Musical
Audio Using an Allpass Filter Chain",
https://ieeexplore.ieee.org/document/6516022
