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

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

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

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

snip


While it might not be obvious, the two cases I
described are basically identical. And this
situation occurs in real life, i.e. in radio signals,
oceanography, and guitar tuning.

The beat you hear during guitar tuning is not modulation;
there
is
no
non-linear process involved (i.e. no multiplication).

Isaac

In short, the human auditory system is not linear.
It has a finite resolution bandwidth. It can't resolve
two tones separted by a few Hertz as two separate tones.
(But if they are separted by 100 Hz they can easily
be separated without hearing a beat.)

Two tones 100 Hz apart may or may not be perceived separately;
depends
on a lot of other factors. MP3 encoding, for example, depends on
the
ear's (very predictable) inability to discern tones "nearby" to
other,
louder ones.

I'll remember that the next time I'm tuning
an MP3 guitar.


The same affect can be seen on a spectrum analyzer.
Give it two frequencies separated by 1 Hz. Set the
resolution bandwidth to 10 Hz. You'll see the peak
rise and fall at 1 Hz.

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

Isaac

What does a spectrum analyzer use to arive at
amplitude values? An envelope detector?
Is that linear?

I'm sure there's more than one way to do it, but I feel certain that
any

Which of them is linear?

A well-designed filter running into a bolometer would be. You can make
the filter narrow enough to respond to only one frequency component at

Any real spectrum analyzer has a lower limit
to its resolution bandwidth, does it not?
The resolution bandwidth of the human ear is non-zero
and not really adjustable, is it not?

the time, and a bolometer just turns the signal power into heat;
nothing
nonlinear there...

Really?
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?

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?


That's all.

Isaac