What exactly causes harmonics?

I generated a 1000 Hz wave in Goldwave and viewed its spectrum - no
harmonics.

Then I sent it through a comm system and viewed the output spectrum -
saw a spike at 2000 Hz (as well as the obvious one at 1000 Hz).

Any ideas?

spake thus:

What exactly causes harmonics?

I generated a 1000 Hz wave in Goldwave and viewed its spectrum - no
harmonics.

Then I sent it through a comm system and viewed the output spectrum -
saw a spike at 2000 Hz (as well as the obvious one at 1000 Hz).

Isn't that, like, a textook case of harmonic distortion?


--
Pierre, mon ami. Jetez encore un Scientologiste
dans le baquet d'acide.

- from a posting in alt.religion.scientology titled
"France recommends dissolving Scientologists"

wrote:
What exactly causes harmonics?

I generated a 1000 Hz wave in Goldwave and viewed its spectrum - no
harmonics.

Then I sent it through a comm system and viewed the output spectrum -
saw a spike at 2000 Hz (as well as the obvious one at 1000 Hz).

Well, technically speaking, it;'s due to a second-order non-
linearity in the comm system., i.e., it's "distorting."

If the comm system were perfect, there would be an exactly
proportional relation between any given input voltage and the
corresponding output voltage. Mathematically, the output
is related to the input as:

Vout = g*Vin + k + Vnoise

which means the output voltage at any given instant is equal
to the gain (g) times the input voltage plus a constant offset
voltage (which cloud or should be 0). If this is what the system
is doing, then it cannot be generating the second harmoncc
spike that you are seeing.

Instead, because we see a 2000 Hz tone, the system is exhibiting
second-order "nonlinearity." Methematically, the output voltage
is related to the input voltage as:

Vout = a*Vin^2 + b*Vin + c

where a and b are coefficients for the various terms, in the
same way that g is a gain coefficient above.

Basically, as said above, your comm system, because of
its non-linearity, is introducing distortion.

Why it is, wothout a LOT more information, is a pure guess.

You aren't, by any chance, working on a school project, are you?

wrote in message
oups.com...
What exactly causes harmonics?
A non-linear amplifier.
Jim

I generated a 1000 Hz wave in Goldwave and viewed its spectrum - no
harmonics.

Then I sent it through a comm system and viewed the output spectrum -
saw a spike at 2000 Hz (as well as the obvious one at 1000 Hz).

Any ideas?

wrote in message
oups.com...
You aren't, by any chance, working on a school project, are you?

That was my guess after his first post. It looks even more likely now.

MrT.

Mr.T spake thus:

wrote in message
oups.com...

You aren't, by any chance, working on a school project, are you?

That was my guess after his first post. It looks even more likely now.

So what's the going rate for doing someone's homework these days?


--
Pierre, mon ami. Jetez encore un Scientologiste
dans le baquet d'acide.

- from a posting in alt.religion.scientology titled
"France recommends dissolving Scientologists"