stupid envelope follower idea

[Magnus Danielson]

From: "Ian Fritz" <ijfritz at earthlink.net>
Subject: Re: stupid envelope follower idea
Date: Wed, 22 Nov 2000 19:53:34 -0700

> Hi Terry --
> 
> > RMS detection is a means of calculating the "area under the curve" of the
> > waveform.
> 
> Huh?  :-)
> 
> The area under the curve of a waveform is zero. (Assuming ac coupling, or,
> equivalently, ignoring the zero frequency Fourier component.)
> 
> > It is commonly done by squaring the instantaneous points of the
> > waveform with an analog multiplier.  The peak voltage squared yields the
> > RMS power.
> 
> Well -- it's (1) square the voltage, (2) average over a cycle, then (3) take
> the square root.

It is Root Mean Square!

The formula is
      ___________
     / 
    /  /     2
\  /   | V(t)  dt  = V
 \/   /               rms
 
 ^     ^     ^
 |     |     |
 Root  Mean  Square

Velly simple.

It actually average the power. Thus, we use square to get the power
and squareroot to get voltage back.

> 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.

It does care, but ONLY in a measurement when you average over a short
waveform, this is a measurement misstake. I mean, if you have a
waveform of 1 Hz and measure 200 ms of it, you are of... you must
always measure a number of cycles or know that you measure a whole
multiple of cycles.

> > 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.

In theory no, in practice too if you don't make big misstakes, for
audio this is not very likely thought.

Cheers,
Magnus