Does perfect white noise really exist?

point taken......

but even if there were an hypothetical point in space enemating pure
white noise (as defined by completely independent and random samples,
with 0 rxx and a completely flat PSD from -inf to +inf, and thereby
giving Einstein's Special Theory of Relativity a complete toss), the
point is that given the current state and future probable direction of
solid state physics, the very act of measuring "pure white noise" to
determine its "(pure) whiteness" will render it non-white.

Partho


Randy Yates wrote:
> Ben wrote:
> > Wondering what ZPMs are??? Zener P----- M------???? or something else?
>
> Oh my - you never watched Stargate SG1 (or Stargate Atlantis)? :)
>
> Zero-Point Modules. - a power supply the size of a pickle jar
> that can power an entire planet.
>
> --Randy
>
>
> >
> > Partho
> >
> >
> > Randy Yates wrote:
> > > Ben wrote:
> > > > [...]
> > > > Then how may the existence of pure white noise be verified, if it ever
> > > > exists in nature, or is it just another mathematical contraption to
> > > > simplify signal modeling?
> > >
> > > We know it doesn't exist by logic. A white noise source
> > > requires infinite power, and there are no infinite power
> > > sources. (ZPMs come close, though...)
> > >
> > > This is a mathemtical contraption, very much like the
> > > Dirac delta function. 
> > > 
> > > --Randy

Ben wrote:
> point taken......
>
> but even if there were an hypothetical point in space enemating pure
> white noise (as defined by completely independent and random samples,
> with 0 rxx and a completely flat PSD from -inf to +inf, and thereby
> giving Einstein's Special Theory of Relativity a complete toss), the
> point is that given the current state and future probable direction of
> solid state physics, the very act of measuring "pure white noise" to
> determine its "(pure) whiteness" will render it non-white.

Ahem. Let me get this straight. You're saying, even if we break
a few laws of physics and discover there is a white noise source,
then, by the laws of physics, measuring it would make it non-white?

YYYYYeahhh. Rrrrrrigggght.

--RY

Tim Wescott wrote:
(snip)

> AFAIK this argument was one of the paradoxes in then-current theory that 
> motivated Plank's theory of black body radiation, and started off the 
> study of quantum mechanics.  Unfortunately I absolutely can't remember 
> where I saw this.

http://en.wikipedia.org/wiki/Ultraviolet_catastrophe

-- glen

;-)

There goes my theory in the trash can!!! But, yes no harm in
hypothesizing half of physics and keeping the other half intact!!!


Randy Yates wrote:
> Ben wrote:
> > point taken......
> >
> > but even if there were an hypothetical point in space enemating pure
> > white noise (as defined by completely independent and random samples,
> > with 0 rxx and a completely flat PSD from -inf to +inf, and thereby
> > giving Einstein's Special Theory of Relativity a complete toss), the
> > point is that given the current state and future probable direction of
> > solid state physics, the very act of measuring "pure white noise" to
> > determine its "(pure) whiteness" will render it non-white.
>
> Ahem. Let me get this straight. You're saying, even if we break
> a few laws of physics and discover there is a white noise source,
> then, by the laws of physics, measuring it would make it non-white?
> 
> YYYYYeahhh. Rrrrrrigggght.
> 
> --RY

Ben wrote:
> point taken......
>
> but even if there were an hypothetical point in space enemating pure
> white noise (as defined by completely independent and random samples,
> with 0 rxx

PS: The autocorrelation of white noise is not 0. 

--Randy

ok there goes my theory in the trash can......I know what you mean, but
no harm in hypothesizing!!!

Randy Yates wrote:
> Ben wrote:
> > point taken......
> >
> > but even if there were an hypothetical point in space enemating pure
> > white noise (as defined by completely independent and random samples,
> > with 0 rxx and a completely flat PSD from -inf to +inf, and thereby
> > giving Einstein's Special Theory of Relativity a complete toss), the
> > point is that given the current state and future probable direction of
> > solid state physics, the very act of measuring "pure white noise" to
> > determine its "(pure) whiteness" will render it non-white.
>
> Ahem. Let me get this straight. You're saying, even if we break
> a few laws of physics and discover there is a white noise source,
> then, by the laws of physics, measuring it would make it non-white?
> 
> YYYYYeahhh. Rrrrrrigggght.
> 
> --RY

sorry I meant unit dirac (delta func).....that way the fft is a flat
band from -inf to +inf

Partho


Randy Yates wrote:
> Ben wrote:
> > point taken......
> >
> > but even if there were an hypothetical point in space enemating pure
> > white noise (as defined by completely independent and random samples,
> > with 0 rxx
> 
> PS: The autocorrelation of white noise is not 0. 
> 
> --Randy

OK, here is a rephrase:

We now know for sure that "pure white noise" is a hypothetical entity,
used for mathematical simplicity rather than any practical use. By
definition, such a source should have an infinite PSD and unit dirac
autocorr (rxx).

Since the PSD (W/Hz) is infinitely flat, the total power consumed by
the noise generator is infinite, which is impossible. So let us assume
a "colored" noise generator with an extremely large, but finite,
bandwidth, much larger than the most prolific measuring instrument
available to us. Since the bandwidth of the measured noise is finitely
large, the autocorr, rxx of the noise process is finitely small, though
not delta.

Let us assume for simplicity sake that rxx in our case is (2k+1)
samples wide - k samples to either side of the current sample r(n).
Hence the correlation occurs from r(n-k) to r(n+k).

In simpler terms, noise sample r(n) for any n >= 0 is correlated to
different extents with all samples in the range r(n-k) and r(n+k), but
is not correlated with samples r(n-k-1) and r(n+k+1) and so on.

So assuming an infinite "colored" noise sequence, the (equally
infinite) subset of every kth sample are all mutually uncorrelated!!!

So let us down sample the noise sequence to obtain this so called
"mutually uncorrelated noise"? What my confusion is that the down
sampling process LPFs the spectrum of the output noise sequence. So
would that affect the premise that the down sampling should have
created a sequence of uncorrelated noise samples in the first place? Is
there some gap in the assumptions or thought process, or am I missing
something here.

Ofcourse, all this is based on the assumption that the auto corr is a
finite sequence for "colored" noise instead of being infinitely
(exponentially) decaying. Is this assumption wrong? Something is amiss
here!!!

Any clarification would be welcome

Partho



Randy Yates wrote:
> Ben wrote:
> > point taken......
> >
> > but even if there were an hypothetical point in space enemating pure
> > white noise (as defined by completely independent and random samples,
> > with 0 rxx and a completely flat PSD from -inf to +inf, and thereby
> > giving Einstein's Special Theory of Relativity a complete toss), the
> > point is that given the current state and future probable direction of
> > solid state physics, the very act of measuring "pure white noise" to
> > determine its "(pure) whiteness" will render it non-white.
>
> Ahem. Let me get this straight. You're saying, even if we break
> a few laws of physics and discover there is a white noise source,
> then, by the laws of physics, measuring it would make it non-white?
> 
> YYYYYeahhh. Rrrrrrigggght.
> 
> --RY

Ben wrote:
> OK, here is a rephrase:
> 
> We now know for sure that "pure white noise" is a hypothetical entity,
> used for mathematical simplicity rather than any practical use. 

   ...

Not quite. Its mathematical simplicity is what makes it practically useful.

Jerry
-- 
Engineering is the art of making what you want from things you can get.
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