Andor wrote:> Tim Wescott wrote: > >> Consider: if you had real, true white noise its power would be infinite >> (finite PSD * infinite bandwidth = infinity). Infinite power implies >> infinite amplitude. Sample that infinite amplitude signal, and all of a >> sudden you've folded up that infinite spectrum into a finite one via >> aliasing, your sample magnitudes are infinite, and you have no way of >> pulling your signal out of the noise. > > Uh, are you saying that a continuous time white noise process has > infinite amplitude because it has infinite power?If all that power is folded into a finite band by sapling ... Once infinite power is admitted, all sorts of paradoxes can follow. In other words, if the moon is made of green cheese, Bob's your uncle. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Effect of Upsampling on White Noise
Started by ●November 11, 2008
Reply by ●November 12, 20082008-11-12
Reply by ●November 13, 20082008-11-13
On Wed, 12 Nov 2008 04:22:05 -0800, Andor wrote:> Tim Wescott wrote: > >> Consider: if you had real, true white noise its power would be infinite >> (finite PSD * infinite bandwidth = infinity). Infinite power implies >> infinite amplitude. Sample that infinite amplitude signal, and all of >> a sudden you've folded up that infinite spectrum into a finite one via >> aliasing, your sample magnitudes are infinite, and you have no way of >> pulling your signal out of the noise. > > Uh, are you saying that a continuous time white noise process has > infinite amplitude because it has infinite power?Yes. Which is how we know that continuous-time white noise processes simply don't exist in the real 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
Reply by ●November 13, 20082008-11-13
On Wed, 12 Nov 2008 13:40:33 -0500, Jerry Avins wrote:> Tim Wescott wrote: > > ... > >> * Namely, white noise is principally useful as an approximation for >> "noise with a bandwidth that's way bigger than my system's bandwidth". > > Why "way bigger"? wouldn't "at least as big as" do? > > JerryIf you say "bandwidth" then you have to have an argument over whether you mean "3dB bandwidth", in which case the upper noise frequency has to be way bigger, or "the uppermost frequency at which my system passes any significant amount of energy". "Way bigger" is easier to say than "at least as big as the uppermost frequency at which my system passes any significant amount of energy", and it works even if your state system "bandwidth" is the 1/2dB rolloff point. -- 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
Reply by ●November 13, 20082008-11-13
On 13 Nov., 16:23, Tim Wescott <t...@seemywebsite.com> wrote:> On Wed, 12 Nov 2008 04:22:05 -0800, Andor wrote: > > Tim Wescott wrote: > > >> Consider: if you had real, true white noise its power would be infinite > >> (finite PSD * infinite bandwidth = infinity). �Infinite power implies > >> infinite amplitude. �Sample that infinite amplitude signal, and all of > >> a sudden you've folded up that infinite spectrum into a finite one via > >> aliasing, your sample magnitudes are infinite, and you have no way of > >> pulling your signal out of the noise. > > > Uh, are you saying that a continuous time white noise process has > > infinite amplitude because it has infinite power? > > Yes. > > Which is how we know that continuous-time white noise processes simply > don't exist in the real world.So to put it really bluntly, if w(t) is a continuous-time white noise process, then w(t) = infinity for all t?
Reply by ●November 13, 20082008-11-13
On Nov 13, 7:33 am, Andor <andor.bari...@gmail.com> wrote:>... > > So to put it really bluntly, if w(t) is a continuous-time white noise > process, then > > w(t) = infinity > > for all t?Or perhaps, the integral of the square of w(t) over finite intervals = infinity. Dale B. Dalrymple
Reply by ●November 13, 20082008-11-13
On Nov 13, 10:33�am, Andor <andor.bari...@gmail.com> wrote:> On 13 Nov., 16:23, Tim Wescott <t...@seemywebsite.com> wrote: > > > > > > > On Wed, 12 Nov 2008 04:22:05 -0800, Andor wrote: > > > Tim Wescott wrote: > > > >> Consider: if you had real, true white noise its power would be infinite > > >> (finite PSD * infinite bandwidth = infinity). �Infinite power implies > > >> infinite amplitude. �Sample that infinite amplitude signal, and all of > > >> a sudden you've folded up that infinite spectrum into a finite one via > > >> aliasing, your sample magnitudes are infinite, and you have no way of > > >> pulling your signal out of the noise. > > > > Uh, are you saying that a continuous time white noise process has > > > infinite amplitude because it has infinite power? > > > Yes. > > > Which is how we know that continuous-time white noise processes simply > > don't exist in the real world. > > So to put it really bluntly, if w(t) is a continuous-time white noise > process, then > > w(t) = infinity > > for all t?- Hide quoted text - > > - Show quoted text -Hello Andor, You may want to look up the "ultraviolet catastrophe" to see about the problem with infinite frequency extent resulting in infinite energy unless something special happens. Planc's solution to the problem was rather unique -- even more amazing is the expression for entropy that he seems to have pulled out of midair. Clay
Reply by ●November 13, 20082008-11-13
On Thu, 13 Nov 2008 07:33:04 -0800, Andor wrote:> On 13 Nov., 16:23, Tim Wescott <t...@seemywebsite.com> wrote: >> On Wed, 12 Nov 2008 04:22:05 -0800, Andor wrote: >> > Tim Wescott wrote: >> >> >> Consider: if you had real, true white noise its power would be >> >> infinite (finite PSD * infinite bandwidth = infinity). Infinite >> >> power implies infinite amplitude. Sample that infinite amplitude >> >> signal, and all of a sudden you've folded up that infinite spectrum >> >> into a finite one via aliasing, your sample magnitudes are infinite, >> >> and you have no way of pulling your signal out of the noise. >> >> > Uh, are you saying that a continuous time white noise process has >> > infinite amplitude because it has infinite power? >> >> Yes. >> >> Which is how we know that continuous-time white noise processes simply >> don't exist in the real world. > > So to put it really bluntly, if w(t) is a continuous-time white noise > process, then > > w(t) = infinity > > for all t?Well, it's a random variable, so it's hard to say that any one _sample_ takes on any particular value. But E{|w(t)|} = infinity certainly holds. And w(t) = +/- infinity probably does, too, but it makes my brain cramp. -- 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
