"isw" wrote in message
...
In article ,
"Ron Baker, Pluralitas!" wrote:

"isw" wrote in message
...
In article ,
"Ron Baker, Pluralitas!" wrote:


--snippety-snip--

You said you are a physicist/engineer.
What does "linear" mean?

Let's not get too far off the subject here. We were discussing
whether
the "tuning beat" that you use to tune a musical instrument involved
a
nonlinear process (ie. "modulation").

Then linearity is at the core of the matter.
What does "linear" (or "nonlinear") mean to you?

OK, if you insist -- *in this case* it means "linear enough to not
produce IM products of significant amplitude".

Good enough.
Then spectrum analyzers and the human auditory
system are not linear.
Stay with me here.


I said that it does not, and that
it could be detected by instrumentation which was proveably linear
(i.e.
not "perfectly" linear, because that's not required, but certainly
linear enough to discount the requirement for "modulation").

No nonlinearity is necessary in order to hear
a beat?
Where does the beat come from?

As the phase of the two nearly equal waves move past each other, there
is simple vector summation which varies the amplitude.

Consider two sine waves of precisely the same frequency, where one of
them is adjustable in phase -- use a goniometer, for instance. Use a
set
of resistors to sum the two signals, and observe the summing point with
a 'scope or a loudspeaker. By altering the phase of one source, you can
get any amplitude you want from zero up to twice the amplitude of
either
one.

Now just twiddle that phase knob around and around as fast as you can.

You've just slightly altered the instantaneous frequency of one of the
generators (but only while you twiddle), and accomplished pretty much
the same effect as listening to the beat between two guitar strings at
nearly zero frequency offset. With no nonlinear processes in sight.

Isaac

You put some effort into that. I give you
credit for that.

The socratic thing isn't working, so here
you go.

I would appreciate it if you would take the time to list *in detail* any
errors in what I wrote. If it "isn't working", I need to know why,
because I don't like to be confused about things.

Is an envelope detector linear? The answer is no.

That's correct, and I'm well aware of it, but so what?

No you're not.

"Yup. And the spectrum analyzer is (hopefully) a very linear system,
producing no intermodulation of its own."

Hopefully?

Is a spectrum analyzer linear?
"I'm sure there's more than one way to do it, but I feel certain..."
Dodging the question.

Which of them is linear?

"a bolometer just turns the signal power into heat; nothing
nonlinear there..."

(Bolometers are no more linear than envelope detectors.)

What does "linear" mean?

"Let's not get too far off the subject here."

Dodging the subject because you don't
understand the subject.



--dissertation on how an envelope detector works snipped--

Vain "editing".


Do you see how this applies to spectrum analyzers
and the human auditory system?

Sure. But

1) It is possible -- if not practical -- to build a "detectorless" (in
the nonlinear process sense) spectrum analyzer, and

Red herring.


2) None of it is even remotely significant to the subject at hand.

A repeat of your earlier dodging.


Here it is again: the "beat" one hears when tuning a guitar or other
instrument does *not* require any nonlinear process for its production.
Period.

You didn't know a spectrum analyzer is nonlinear.
You didn't/don't know that a bolometer is nonlinear.
You wouldn't and don't know nonlinearity even when you
hear it.


Isaac

You are a poseur.