[sdiy] VCO reset time

[Magnus Danielson]

From: "JH." <jhaible at debitel.net>
Subject: Re: [sdiy] VCO reset time
Date: Sun, 6 Jun 2004 21:02:31 +0200
Message-ID: <000b01c44bf8$f551ae00$4e7fb9d9 at jhsilent>

Hi Jürgen,

> The two of you have convinced me.

Great! ;O)

> So there is no angle modulation involved.

No.

> What I remembered was that there are sidebands on the harmonics
> (not the fundamental) created - much less than in the saw pwm case,
> but still there. Of course the sidebands are completely explained
> by AM - no FM/PM needed.

Indeed.

> The "moving notches" (comb filter effect) can certainly be traced back to
> AM as well.

Actually no, they are explain fully by the pure static-case of a tri-based
PWM. The notches moves because of the changed PWM factor alpha changes the
"speed" of the sine setting the overtone spectrum. The comb-filter effect is
thus not an effect of summing of differently phased or time-delayed variants of
a signal. However, when we move the notches then we do experience AM, but the
AM does not explain for the notches. 

> The sidebands which are created from modulation (as opposed to
> simple waveform / sound changes of a very slow, quasi static 
> PW change) are responsible for the remaining chorusing / detuned
> effect. It's more prominent at low notes (for a fixed PWM rate
> and depth), as the relative frequency deviation from sidebands
> of harmonics to original harmonics is bigger there.

Indeed.

Now comes a point I'm trying to make a number of times. If we modulate the
PWM of a tri-based PWM with a simple sine, then each overtone (including the
fundamental) will be have an AM-modulation and I might also want to point out
that this may even be seen having 4-quadrant properties. Anyway, this will
cause us to see the traditional sidebands.

However, let's for a moment assume that we instead of modulating it with a
sine LFO uses an envelope generator that we trigger ONCE during the sound.
This effect is certainly audioble, we will preceive it, but trying to analyse
the spectrum of this one is a lost cause. The "spectrum" view on things is no
longer valid since we do change amplitudes of the overtones with a filtered
impulse. So, even if we excell in explaining things in the spectral form we
must recall the impulse-oriented and non-static world we are really part of.

The use of LaPlace transforms over Fourier transforms is one such step, but it
doesn't handle the non-linear or time-variant aspects of the systems we often
find us fiddeling around with. Such a step is still necessary for additional
insight. Fourier is nice, usefull and wonderfull for many bread-and-butter
applications (we should not really promote such bad food-habbits but anyway)
but for full power you need more, much more.

Cheers,
Magnus