I see what you mean, but I can't help but feel that this is missing the point of pondering the topic of magnitude distortion of an analytic signal, which is that even if the output derives entirely from the input real-valued signal it's quite different from normal distortion and has different properties which presumably result a different audio effect and this is probably worth investigating if this hasn't already been done. Applying distortion to the radius of a spinning signal is very much the idea, in fact I'd wager that applying that to complex signals that aren't analytic signals but that wiggle every which way in the complex plane instead of just spinning in one direction would be more similar to regular distortion and give a less novel effect.Since the imaginary component y has been made up with a Hilbert transform, it depends on x and doesn't contain any additional information, so your gain a actually depends on x only.But that's wrong, a(t) would be a function of sqrt(x(t)^2+y(t)^2).
You should probably try actual complex signals (for example, upgrading a synth to nontrivial quadrature oscillators), using Hilbert transforms of real signals as a fallback for mono inputs and/or as a test case.
The aspect about applying this specifically to analytic signals and that made me think it could be interesting is specifically that the real output would be just as affected around zero as it would be around the extrema which would make sinusoids remain sinusoids, whereas with regular distortion values around zero remain unchanged and sinusoids stop being sinusoids, they get flat tops and sharp corners. It's an effect that instead flattening all the peaks would tend to make signals more wavy. I think that a non-analytic complex signal might fall between the two (kind of flat-topped with sharp corners, kind of wavy), so doing this on analytic signals is the more novel and pure effect.
Statistics: Posted by A_SN — Fri Mar 22, 2024 11:12 am