From: "John S. Dyson"
Subject: Re: How does a mixer work?
X-Newsreader: Microsoft Outlook Express 6.00.2800.1106
Date: Tue, 22 Oct 2002 18:38:59 -0500
NNTP-Posting-Date: Tue, 22 Oct 2002 18:32:27 EST
"Dbowey" wrote in message news:email@example.com...
> John Woodgate posted:
> << The carrier amplitude is constant IF you also take into account the
> sidebands as separate signals. >>
> Since the sidebands ARE separate signals, you have put a point on my attempted
> arguments on this subject. Thanks.
> He also posted:
> "People simply continue to confuse two wholly-equivalent representations of
> the signal and then claim that one is invalid."
(This response is not meant to refute the posting that I am responding to,
and I am NOT trying to educate those who already probably know more
about the stuff than I do, but I am trying to clarify this in a pseudo-laymans
sense.) EVERY ONE OF MY ASSERTIONS IS MADE FROM THE VIEW
OF THE WORKING ENGINEER, and I am not trying to define the one, true
11 or 13 (or somesuch) true reality!!! :-).
Okay -- I think that I understand the basis of this really unpleasant discussion,
but will try to clarify my own opinion (each of us has one :-)).
Firstly, the real world signal (as we normally perceive it) is in the time domain.
Any normal means of spectrum analysis, or fourier transform tends to make
the assumption that the function is non-varying in character. Additionally, the
normal linear transforms (where spectrum analysis is allied to the fourier
kind of transform) don't generally work well WRT nonlinear operations (or
with signals that have time varying characteristics.) Spectrum analysis or
fourier transforms can still be useful in varying situations, but the information
needs to be interpreted slightly differently, and with some caveats.
When 'modulating' for AM, that operation is nonlinear in the time domain. Indeed,
the carrier level is definitely changed (in the time domain) in simple AM. When
looking at an AM signal represented on an f(t) type display, you'll see a
representation of the changing carrier level. Also, it is possible to
collect characteristics of a modulated signal, and display those in the form
of a spectrum. The f(w) type spectrum is quite useful at times, but has
limitations in displaying the full characterization of physical processes,
much as the laplace domain doesn't generally work well in solving
As an argument for the usefulness of the fourier spectrum, and to prove that
the spectra of a modulated signal is representative: Imagine a keyed or
modulated carrier of somesort. Then, view the spectrum in f(w), you'll
notice that there is often a carrier, and will often be sidebands (depending
upon the kind of modulation.) For a 'really good time', in order to give
an example of even the degenerate amplitude modulation: CW morse
code type stuff. You can do an f(w) resolution of the signal. Now,
instead of using a normal 100-500Hz filter for CW (which maintains
the keying modulation), you can do a super sharp filter at the carrier
frequency. The output of the filter will be a continuous carrier (well,
if there is enough carrier left after keying), because of the 'technologists'
view of the filter's Q factor. With the sharp filter, the modulation
(keying on/off) will almost be totally obliterated, where it will be picking
out only the carrier frequency. The nature of a filter 'ringing' or persisting
in providing an output (after being excited by a signal) is roughly
equivalent to removing the sidebands necessary to represent a changing
level of the AM signal!!!
However, in a non-steady state condition, the spectrum isn't quite as
illuminating (but still somewhat useful) as when using the 'spectrum' with
an f(t) signal with unchanging characteristics. Theoretically, you can
do the f(t) <-> f(w) transform, however the usefulness of the spectrum
for the purposes of visualizing things like 'carriers and sidebands' can
be slightly unintuitive. Considering the fact that the various signals
do change in their statistics, and that many systems are nonlinear,
it is wise to have skills that allow for working in the f(t) domain to
solve and describe nonlinear systems.
Since the real world f(t) is the result of nonlinear operations, and the operations
on that f(t) are nonlinear in a lot of ways, the simple fourier spectrum
viewpoint is inadequate in general, and is easy to misuse. There are
ways of applying some well known time domain nonlinear operations for
the fourier domain and estimating the resulting fourier spectrum, but those methods
aren't very general. This is ALMOST exactly the same as trying to apply
laplace in nonlinear situations.
I am NOT making the cosmological assertion that everything is really
an f(t) or other such off-topic concerns, but am clearly stating that much
of our real-world that we normally see (in the sense of this discussion)
is an f(t). f(w) or f(s) is a convienience, where nonlinear operations
or changing signal characteristics can cause some traps and/or pitfalls
for those who don't deal with the stuff all of the time.