George Dishman says Karl Uppiano is wrong about AM radio, carrier-
frequencies, and aliasing. Who should I believe and why?

On Jul 14, 4:11 pm, "George Dishman" wrote
in http://groups.google.com/group/sci.a...05843c0?hl=en&
:
"Radium" wrote in message

oups.com...

On Jul 14, 1:17 am, "George Dishman" wrote:
"Radium" wrote in message

groups.com...
..

Isn't it true that the carrier-frequency must be at least 2x the
highest intended frequency of the modulator signal?

No.

Karl Uppiano sharply disagrees.

Karl Uppiano explained in
http://groups.google.com/group/sci.e...cea47a5?hl=en&

He is wrong. The basis of AM is that the sine wave
carrier is multiplied by another signal which can be
treated as a sum of sines. The relevant maths is:

http://www.sosmath.com/trig/prodform/prodform.html

If the carrier frequency if fc and the modulation has
frequencies up to fm then you get sidebands like
this:

http://en.wikipedia.org/wiki/Image:Am-sidebands.png

If you multiply 44.1kHz by a band from 20Hz to 20kHz,
you get an upper sideband given 44.12kHz to 64.1kHz
and a lower sideband from 44.08kHz down to 24.1kHz

The highest modulating frequency for AM must be less than 1/2 the carrier
frequency. Conversely, the lowest carrier frequency must be twice the
highest modulating frequency. Period. I don't care what specific
frequencies
and/or energies and/or colors you propose.

If you want to modulate at 20KHz, the carrier must be at least 40KHz. It
is
no coincidence that CD audio uses a 44.1KHz sample rate. It is
essentially
the same principle. If you exceed the Nyquist criterion, the sidebands
overlap the baseband (i.e., aliasing occurs) and you cannot unambiguously
decode the original modulation.

Nyquist applies to sampling.

So who is right and who is wrong?

Look at the maths, it is never wrong. Modulating fc
with fm gives a lowest frequency of fc-fm so as long
as fc fm, you don't get aliasing.

George

So is it possible for me to receive a 10 KHz audio sine-wave tone on a
1 Hz AM radio receiver? If not, why? My guess is it violates Nyquist/
Shannon. Right?