DSP and Plugin Development • Re: Distortion of an analytic signal - has this been tried?

As I noted above (with sketch of proof too) those spikes would be infinite for a theoretically perfect sawtooth ...

That's interesting. It implies that the instantaneous envelope defined as sqrt(x^2 + y^2) also becomes infinite at these instants. That's a weird feature for a signal that goes by the name "instantaneous envelope". For a saw, that "envelope" looks nothing like what one would intuitively draw in as envelope - i.e. the envelope with which the saw was synthesized. The terminology seems to make sense only for sinusoids.

Do you have any idea about the stairstep artifacts? Is this normal or should I be worried that my implementation is wrong?

"Envelopes" being the magnitude of a sound's analytic signal isn't necessarily the smooth synthesis envelope we picture, the "envelope" of a wide bandwidth signal is gonna have a wide bandwidth too. It only matches what we picture when dealing with very narrow band signals because then the magnitude of the analytic signal is as if we took the analytic signal and completely untwisted it flat. In a way this "envelope" shows you the reality of sawtooth waves which is that they're a pretty spiky thing that also twists (unlike pure tones that are flat but spin regularly), and the more harmonics you have the more the spikes are high and sharp. And our analytic distortion caps those spikes.

The "artifacts" you get are probably the ripples from the processing the bandlimited sawtooth, maybe aliasing has an effect too. Honestly you should do like me, take the continuous pill, synthesise sawtooths sine by sine (I could have used that opportunity to apply a Gaussian window on their intensities to make a ripple-free graph btw) and their Hilbert transform in the same way, then things get clearer. I'm so continuous-pilled I don't even want to process sounds as samples anymore, I'd rather turn them into polynomial chunks and never deal with an accursed sample again.

Anyway since you did the work with sampled signals, have you tried the concept on real sounds?

Statistics: Posted by A_SN — Sun Mar 24, 2024 11:45 am

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