Re: Additive White Gaussian Noise Question

On Fri, 05 Oct 2007 00:17:41 -0700, Necronomicon wrote:

On Oct 4, 7:40 pm, Tim Wescott <t...@xxxxxxxxxxxxxxxx> wrote:
On Thu, 04 Oct 2007 16:33:55 -0700, Necronomicon wrote:
My understanding is that when you add AWGN to a carrier,
you make the amplitude a gaussian distribution, and then
add white noise to this (not really pure white noise, but as
high a BW as your simulation can handle).

If you are doing simulation, and not analysis or real-world measurements,
yes.



However, if you amplitude modulate a carrier by any AM % modulation,
then your Fourier transform will show side bands which will not be
spectrally flat like the added white noise.

That depends on how you're amplitude modulating the carrier -- "amplitude
modulate" it with white noise & you'll get spectrally flat "side bands"
(actually you'll spread the carrier energy all over every place).


My point is that if you add the gaussian noise to the
amplitude, the side bands will not be spectrally flat.

That statement is either meaningless or wrong, depending on how you
constrain things. If by "adding Gaussian noise to the amplitude" you mean
carrying out textbook AM modulation as I've defined it below, then no,
you're wrong, white Gaussian noise will result in flat sidebands. Even
band-limited Gaussian noise with a flat-topped spectrum will result in
sidebands that are spectrally flat within their bandwidth.

If you disagree, please demonstrate you superior knowledge with
mathematics, not words.

I use the quote marks because the amplitude of white noise is infinite,
while regular old AM (A1x modulation) demands that the modulating signal
be bounded. But if you generate a signal as (1 + x(t)) * sin(w * t), and
x(t) is white noise, then you'll splatter your signal evenly from DC to
light.

(this indicates how we get
AM-to-PM effects, and also makes AM seem a bit of a misnomer, because in
actuality you still alter the frequency spectrum. Whereas you can strip
the AM off an FM signal, and still not lose information).

_Any_ modulation will alter the frequency spectrum of a carrier, so I
don't see how AM is a misnomer.


My point is that pure FM does not alter the amplitude
while pure AM still alters the frequency spectrum.

A curve in a road changes the direction you're traveling, but almost
never does it change the road name. So what's the point of your point?

So these added side bands from the Gaussian distribution of the
amplitude is what makes AWGN different from just pure white noise on
a carrier, right?

Huh? I'm not even sure what you're asking here.


How would you differentiate AWGN from
simple white noise + carrier?

What do you mean by "simple white noise"? What do you mean by "+"?

If you mean "non-Gaussian white noise arithmetically added to a carrier"
then you could tell that the distribution wasn't Gaussian. If you mean
"Gaussian white noise arithmetically added to a carrier", well that's
AWGN, and you need to think about what you mean when you make these
definitive statements to the wide world.

--
Tim Wescott
Control systems and communications consulting
http://www.wescottdesign.com

Need to learn how to apply control theory in your embedded system?
"Applied Control Theory for Embedded Systems" by Tim Wescott
Elsevier/Newnes, http://www.wescottdesign.com/actfes/actfes.html
.

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