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From: levy@ttrdc.UUCP (Daniel R. Levy)
Newsgroups: net.analog
Subject: Re: Looking for a method to invert a function.
Message-ID: <1215@ttrdc.UUCP>
Date: Mon, 6-Oct-86 00:21:47 EDT
Article-I.D.: ttrdc.1215
Posted: Mon Oct  6 00:21:47 1986
Date-Received: Wed, 8-Oct-86 00:20:53 EDT
References: <343@axiom.UUCP>
Organization: AT&T, Computer Systems Division, Skokie, IL
Lines: 34
Keywords: h(t) = f(t) + h(t) - f(t)

In article <343@axiom.UUCP>, gts@axiom.UUCP (Guy Schafer) writes:
>I'm looking for an analog circuit that can perform two functions:
>
>1. Reflect a function about the x-axis.  That is, turn f(t) into -f(t).
>Where f(t) is the sum of many low frequency (less than 20kHz) sine
>waves.

I don't see what the great trick is here; you are just inverting the signal
polarity!  Now if what you MEAN is to turn f(t) into f(-t) (invert in time)
that's a different story:  If f(t) does not exist before t=0, that's easy;
tie your signal input to ground :-).  If it does exist before t=0, it is
"impossible" to reconstruct anything more about the arbitrary function than
is known in its past history.  If it is presumed the function is periodic
then construction of an approximation to the time-mirror image could be done
by a simple (DIGITAL) sample-and-store-then-reconstruct circuit after
observation of one cycle.

>2. Add -f(t) to another signal, say g(t); where g(t) is a composite
>of two functions: g(t) = f(t) + h(t).
>This will reveal the imbedded signal h(t).
>Any comments about the theoretical sensitivity of this procedure?  How
>much energy must be in signal h(t) compared to f(t)?  Are FFT's required
>to perform step one?  (If this is so, can a digital circuit be constructed?)
>Mail to me, I'll summarize if the CIA lets me.
>	>< ...{ decvax!linus || seismo!harvard }!axiom!gts
>	"Understand or leave."
-- 
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|        skokie, illinois        |
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