Does Gaussian Noise have the highest variance among all possible noise distributions? Is there a way to prove it??
Variance of Gaussian Noise
Started by ●March 25, 2009
Reply by ●March 25, 20092009-03-25
On Mar 25, 2:54�pm, "sasuke" <a.ssjg...@gmail.com> wrote:> Does Gaussian Noise have the highest variance among all possible noise > distributions? Is there a way to prove it??No. No. Your question is not meaningful without adding some limitations/conditions on the noise distributions. spamfree
Reply by ●March 25, 20092009-03-25
On Mar 26, 7:54 am, "sasuke" <a.ssjg...@gmail.com> wrote:> Does Gaussian Noise have the highest variance among all possible noise > distributions? Is there a way to prove it??Isn't that a bit like asking - Does a 24kHz sine wave have the largest amplitude of all frequencies?
Reply by ●March 25, 20092009-03-25
>On Mar 26, 7:54 am, "sasuke" <a.ssjg...@gmail.com> wrote: >> Does Gaussian Noise have the highest variance among all possible noise >> distributions? Is there a way to prove it?? > >Isn't that a bit like asking - Does a 24kHz sine wave have the largest >amplitude of all frequencies? >Sorry. I messed up the question completely. Please disregard. The question which I actually wanted to ask was, is it true that Gaussian noise is the worse kind of noise to affect a communication channel? In other words is the capacity of a communication channel least when the channel is corrupted by an additive Gaussian noise??
Reply by ●March 25, 20092009-03-25
On Mar 25, 6:34�pm, "sasuke" <a.ssjg...@gmail.com> wrote:> >On Mar 26, 7:54 am, "sasuke" <a.ssjg...@gmail.com> wrote: > >> Does Gaussian Noise have the highest variance among all possible noise > >> distributions? Is there a way to prove it?? > > >Isn't that a bit like asking - Does a 24kHz sine wave have the largest > >amplitude of all frequencies? > > Sorry. I messed up the question completely. Please disregard. > The question which I actually wanted to ask was, is it true that Gaussian > noise is the worse kind of noise to affect a communication channel? In > other words is the capacity of a communication channel least when the > channel is corrupted by an additive Gaussian noise??What would happen if your noise looked very much like your signal rather than being Gaussian?
Reply by ●March 25, 20092009-03-25
sasuke schrieb:>> On Mar 26, 7:54 am, "sasuke" <a.ssjg...@gmail.com> wrote: >>> Does Gaussian Noise have the highest variance among all possible noise >>> distributions? Is there a way to prove it?? >> Isn't that a bit like asking - Does a 24kHz sine wave have the largest >> amplitude of all frequencies? >> > > Sorry. I messed up the question completely. Please disregard. > The question which I actually wanted to ask was, is it true that Gaussian > noise is the worse kind of noise to affect a communication channel? In > other words is the capacity of a communication channel least when the > channel is corrupted by an additive Gaussian noise?? >Actually gaussian additive noise is the ideal kind not the worst kind. Because gaussian distributions are simple to be analysed many filters are optimised for that kind of noise. The capacity of the channel will decrease in any case of noise, so your question still sounds confused...
Reply by ●March 26, 20092009-03-26
On Mar 25, 7:08�pm, Sebastian Doht <seb_d...@lycos.com> wrote:> sasuke schrieb: > > >> On Mar 26, 7:54 am, "sasuke" <a.ssjg...@gmail.com> wrote: > >>> Does Gaussian Noise have the highest variance among all possible noise > >>> distributions? Is there a way to prove it?? > >> Isn't that a bit like asking - Does a 24kHz sine wave have the largest > >> amplitude of all frequencies? > > > Sorry. I messed up the question completely. Please disregard. > > The question which I actually wanted to ask was, is it true that Gaussian > > noise is the worse kind of noise to affect a communication channel? In > > other words is the capacity of a communication channel least when the > > channel is corrupted by an additive Gaussian noise?? > > Actually gaussian additive noise is the ideal kind not the worst kind. > Because gaussian distributions are simple to be analysed many filters > are optimised for that kind of noise. > The capacity of the channel will decrease in any case of noise, so your > question still sounds confused...I'll try to interpret your question as given a fixed amount of average power, which amplitude distribution is most effective at jamming. In that case Gaussian noise would not be the answer... I think the answer would be an impulsive noise signal whose BW was confined to your channel of interest and that is either off or on and when on it is at max power and the duration and repetition rate of the on time is such so as to do the most damage based on the FEC the system is using. So the answer depends on the type of FEC. But Gaussian noise while it has infinte peaks (in theory) does not make the "best use" of the average power. Mark
Reply by ●March 26, 20092009-03-26
On Wed, 25 Mar 2009 17:34:22 -0500, sasuke wrote:>>On Mar 26, 7:54 am, "sasuke" <a.ssjg...@gmail.com> wrote: >>> Does Gaussian Noise have the highest variance among all possible noise >>> distributions? Is there a way to prove it?? >> >>Isn't that a bit like asking - Does a 24kHz sine wave have the largest >>amplitude of all frequencies? >> >> > Sorry. I messed up the question completely. Please disregard. The > question which I actually wanted to ask was, is it true that Gaussian > noise is the worse kind of noise to affect a communication channel? In > other words is the capacity of a communication channel least when the > channel is corrupted by an additive Gaussian noise??It's certainly the easiest kind to analyze, and I _think_ it has the lowest possible values for all of the higher-order moments for a given variance (dunno -- have to check). It's hard to say what's "worst", because if you know the noise properties before hand you can design for it. Certainly if you're designing for Gaussian noise and you're hit with noise that has a Cauer-like density (i.e. infinite variance, as you see with atmospheric noise in LF and MF) your receiver will be more than a little confused. -- http://www.wescottdesign.com
Reply by ●March 26, 20092009-03-26
sasuke wrote:> The question which I actually wanted to ask was, is it true that Gaussian > noise is the worse kind of noise to affect a communication channel? In > other words is the capacity of a communication channel least when the > channel is corrupted by an additive Gaussian noise??You are correct. For the given noise power, the AWGN corresponds to the minimum capacity of the communication channel. Any non-AWGN case can be converted to the equivalent Gaussian by means of some linear or non-linear operation with the corresponding increase in the channel capacity. Vladimir Vassilevsky DSP and Mixed Signal Design Consultant http://www.abvolt.com
Reply by ●March 26, 20092009-03-26
sasuke wrote:> The question which I actually wanted to ask was, is it true that Gaussian > noise is the worse kind of noise to affect a communication channel? In > other words is the capacity of a communication channel least when the > channel is corrupted by an additive Gaussian noise??White or colored? bye, -- piergiorgio