stupid envelope follower idea

[Magnus Danielson]

From: Harry Bissell <harrybissell at prodigy.net>
Subject: Re: stupid envelope follower idea
Date: Thu, 23 Nov 2000 00:54:58 -0500

Hi folks,

> > But since the instantaneous power is independent of the phases of the
> > various Fourier components, the phase shifts you are concerned about don't
> > matter. They change the instantaneous waveform amplitude, but not the RMS
> > value.
> >
> > > I hope that's right, I'm going by memory here.   The problem
> > > with that approach might be the time altered waveform might not have the
> > > same "area under the curve" as the original waveform.  It should be
> > > possible to do a mathmatical analysis or simulation to answer your
> > > question, maybe someone on the list has the means to do so, unfortunately
> > I
> > > don't.
> >
> > I think the math is simple. The RMS voltage is the square root of the sum of
> > the squares of the Fourier amplitudes. Phases don't matter.
> 
> OTOH: I bet after you break the signal into bands, RMS each, and sum them
> together...
> that the envelope follower looks a lot like the original signal... unfollowed
> (so to speak)
> But its worth a try. Now I'll have to try and do a simulation on this... that
> should keep
> me busy for a while...

What you should do is to MS each of them (notice the lack of the R!),
sum them together and then R!

That is, you filterbank into diffrent frequency ranges, squares the
signal, average each band (with suitable time-constant, basically
being of the same relation to the cycle time for all bands) sums these
average values (that is, sum the power of each band) and then
finallize by square-rooting to get the voltage level.

Hmm... my vocoder sounds like a good place to consider to do such a
thing... no, it's not - guess why!

Happy simulation!

Cheers,
Magnus