On Fri, 05 Oct 2007 00:17:41 -0700, Necronomicon wrote:> On Oct 4, 7:40 pm, Tim Wescott <t...@seemywebsite.com> 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
Additive White Gaussian Noise Question
Started by ●October 4, 2007
Reply by ●October 5, 20072007-10-05
Reply by ●October 5, 20072007-10-05
Tim Wescott wrote: ...> If you disagree, please demonstrate you superior knowledge with > mathematics, not words....> you need to think about what you mean when you make these > definitive statements to the wide world.Give the kid a break, or at least benefit of doubt. He has some erroneous idea that's messing up his head shielding him from enlightenment. Jerry -- "It ain't what you don't know that hurts so much. The real stinker is what you think you know but just ain't so." ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
Reply by ●October 5, 20072007-10-05
"Necronomicon" <radio913@aol.com> wrote in message news:1191540835.878177.313440@n39g2000hsh.googlegroups.com...> 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). > > 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. (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). > > 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?No. But only because of the terms you're using. Unless otherwise stated, noise is generally treated as a added component of a signal. - which means that each part can be considered all by itself at least analytically. So, when you say "add AWGN to a carrier" that translates into "add additive" white gaussian noise to a carrier. But, since the noise and the carrier are separable in the composition, it doesn't matter if there's a carrier or anything else. The noise is the noise and its spectral character will remain. And, if there's a carrier, then the carrier is the carrier and its spectral character will remain. Note that addition also applies to the spectral components. So, the spectrum of the sum of the two is the sum of the spectra of the two. You confuse me when you go on to say: "and then add white noise to this" I'm confused because you already added white noise. So, this is just *more* white noise? When you add white noise and a carrier, you *don't* make the amplitude distribution gaussian. Consider this: - if the noise amplitude is very small relative to the carrier then the amplitude distribution will be very close to that of the sinusoid. - if the noise amplitude is very large then the amplitude distribution will tend to gaussian. So, when you say:> 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?Unfortunately, wrong. It's the temporal distribution of the noise amplitude that's Gaussian - which says nothing about it's spetral character (which is flat if it's white). AWGN and "JPWN on a carrier" are the same thing if by "on" you mean added - which is the normal situation. Are you trying to somehow differentiate between Added WGN and a carrier modulated with WGN? And, by "modulated" you mean AM? If so then here is a perspective: As above, Added WGN is the typical case. As such it can be separated from a carrier (analytically and practically by filtering .. just not perfectly). And the "W" means the spectrum of the noise is flat. The spectral components add as well. If you want to consider a carrier AM Modulated by WGN then the spectral sidebands, if you will, are flat by virtue of the flat spectral character of the noise. So, when you say:> 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's unfortunately wrong in the case of WGN used for AM modulation of a sinusoid. Perhaps you're confused by the decaying nature of AM sidebands when the modulating signal is audio. The sidebands for AM modulation are but a replica of the modulating signal's spectrum for both positive and negative frequencies. So, if you Modulate with WGN the sidebands will reflect its flat spectral character as well. Here I neglect that the WGN spectrum would be infinite to be "white". I just assume that the bandwidths under discussion are "big enough" for the purpose of discussion. Fred
Reply by ●October 5, 20072007-10-05
On Oct 5, 8:09 am, Tim Wescott <t...@seemywebsite.com> wrote:> On Fri, 05 Oct 2007 00:17:41 -0700, Necronomicon wrote: > > On Oct 4, 7:40 pm, Tim Wescott <t...@seemywebsite.com> 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 consultinghttp://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- Hide quoted text - > > - Show quoted text -- Hide quoted text - > > - Show quoted text -Stick with control systems.....
Reply by ●October 5, 20072007-10-05
On Oct 5, 6:25 am, Mark <makol...@yahoo.com> wrote:> On Oct 4, 7:33 pm, Necronomicon <radio...@aol.com> wrote: > > > My understanding is that when you add AWGN to a carrier, > > you make the amplitude a gaussian distribution, > > You make the amplitude of the NOISE is a Gaussian distribution, not > the carrier. >This is incorrect. The white noise has constant spectral density, expressed as Watts/Hz. The noise spectral density can't be contant if the amplitude is gaussian distributed.
Reply by ●October 6, 20072007-10-06
Necronomicon wrote: ...> Stick with control systems.....Grow up. That's an extremely unbecoming remark for someone as ignorant as you evidently are. Jerry -- Engineering is the art of making what you want from things you can get. ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
Reply by ●October 6, 20072007-10-06
Necronomicon wrote:> On Oct 5, 6:25 am, Mark <makol...@yahoo.com> wrote: >> On Oct 4, 7:33 pm, Necronomicon <radio...@aol.com> wrote: >> >>> My understanding is that when you add AWGN to a carrier, >>> you make the amplitude a gaussian distribution, >> You make the amplitude of the NOISE is a Gaussian distribution, not >> the carrier. >> > > This is incorrect. The white noise has constant spectral > density, expressed as Watts/Hz. The noise spectral > density can't be contant if the amplitude is gaussian distributed.That's flat wrong. Gaussian or not, the noise spectrum is flat if it is white. Where do your cockamamie ideas come from? Jerry -- Engineering is the art of making what you want from things you can get. ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
Reply by ●October 6, 20072007-10-06
Necronomicon <radio913@aol.com> writes:> [...] > The noise spectral density can't be contant if the amplitude is > gaussian distributed.Wrong. The distribution of the noise is independent of its whiteness or lack thereof. Have you ever had a course in stochastic (or random) processes? One of my favorite, accessible books on the subject is [garcia]: @book{garcia, title = "Probability and Random Processes for Electrical Engineering", author = "{Alberto~Leon-Garcia}", publisher = "Addison-Wesley", year = "1989"} -- % Randy Yates % "She tells me that she likes me very much, %% Fuquay-Varina, NC % but when I try to touch, she makes it %%% 919-577-9882 % all too clear." %%%% <yates@ieee.org> % 'Yours Truly, 2095', *Time*, ELO http://www.digitalsignallabs.com
Reply by ●October 6, 20072007-10-06
"Necronomicon" <radio913@aol.com> wrote in message news:1191638927.696573.25010@k79g2000hse.googlegroups.com...> On Oct 5, 6:25 am, Mark <makol...@yahoo.com> wrote: >> On Oct 4, 7:33 pm, Necronomicon <radio...@aol.com> wrote: >> >> > My understanding is that when you add AWGN to a carrier, >> > you make the amplitude a gaussian distribution, >> >> You make the amplitude of the NOISE is a Gaussian distribution, not >> the carrier. >> > > This is incorrect. The white noise has constant spectral > density, expressed as Watts/Hz. The noise spectral > density can't be contant if the amplitude is gaussian distributed.1) You refer to the "white noise" with constant spectral density. 2) You refer to some "noise" with spectral density that can't be constant. These two assertions appear to contradict at face value. So, perhaps you could be more explicit in your terms. Are you confusing WGN (with a Gaussian amplitude distribution) with a Gaussian function? The former has a flat spectral density (thus "white") which goes along with your reference (1). The latter has a Gaussian spectral density which easily meets your reference (2) because it has a Gaussian spectral density .. but it ain't noise. There can be Gaussian noise (the amplitude in time is Gaussian disributed) that's "pink" - meaning it's not white and thus has spectral density that isn't constant. Usually it's a particular form of frequency dependence. So, I suppose that one could have Gaussian noise with the spectral density being Gaussian centered at f=0 but I don't know what that would be called and I've never encountered it. I can't imagine what physical phenomenon would cause such an interesting character. It would be interesting to prove if such noise could exist. Fred
Reply by ●October 6, 20072007-10-06
On Oct 5, 8:51 pm, Randy Yates <ya...@ieee.org> wrote:> Necronomicon <radio...@aol.com> writes: > > [...] > > The noise spectral density can't be contant if the amplitude is > > gaussian distributed. > > Wrong. The distribution of the noise is independent of its whiteness > or lack thereof. >So you think if the amplitude changes, that the wattage will always remain constant??!!?? BWAAHAHAAHHAAAHHAAA!!!
