envelope follower

[Grant Richter]

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> From: CGS2510.SEP.STUDENT.UCA at CUB.UCA.EDU
> To: Grant Richter <grichter at execpc.com>
> Subject: Re: envelope follower
> Date: Thursday, October 02, 1997 7:59 AM
> 
> > Has anyone messed with the "Cepstrum" concept. i.e. take the Log to the
> > signal, filter it then take the anti-Log? This converts the frequency
axis
> > to time (according to Bernie Hutchins) and makes the envelope
components
> > (long time) more easily filterable from the signal components (short
time).
> 
> Whats this?  Who is Bernie Hutchins?  Where can I read about it in
detail?

I went back and rechecked this. The was actually cited in Electronotes #53
in Bernie Hutchins (the editor of Electronotes newsletter) series on pitch
extraction. The original reference is The Journal of the Audio Society of
America (I think that's what JASA stands for) #41 (1967) page 293 "Cepstral
Pitch Determination".

The basic idea is that a complex tone is a signal multiplied by a formant
F(w)=E(w)*H(w) but we also know log F(w)= log E(w) + log H(w) so the
multiplication becomes an addition after taking the log.

I was thinking that a complex signal is a simple signal multiplied by an
envelope (a VCA is a 2 quadrant multiplier) so the same idea would apply. I
probably have this all mixed up, some math whiz please shoot me down. But
what does happen if you take the log of a signal, filter it, and then take
the anti-log?