Does perfect white noise really exist?

Andor wrote:
> Tim Wescott wrote:
> ...
>> 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.
> 
> It's probably one of those things you can't simultaneously know and
> remember where you read it :-).

Too many of those things for me lately. I haven't decided if I remember 
less or know more. (Don't tell me!) I too remember some apparent paradox 
leading to a divergence between Boltzmann's and Planck's formulations.

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

> I think you are right all along:
>
> - Perfect white noise must, if it exists, have a constant PDF
>   on the interval <-inf, inf>
> - Hence it has infinite power
> - Hence its existence is questionable, at best.
> - White noise is a useful *model* for analysis of *bandlimited *
>   systems
> - There s no such thing as a measurement system with a
>   perfect impulse response
>
> Nah, I agree with you on all your points.
>
> Rune

In the first point, I think you meant PDF instead of PSD......it is
precisely because the power (spectral) density (W/Hz) is flat for -inf
to +inf, the total power is infinite....PDF has nothing to do with
power/power density

Partho

> I think you are right all along:
>
> - Perfect white noise must, if it exists, have a constant PDF
>   on the interval <-inf, inf>
> - Hence it has infinite power
> - Hence its existence is questionable, at best.
> - White noise is a useful *model* for analysis of *bandlimited *
>   systems
> - There s no such thing as a measurement system with a
>   perfect impulse response
>
> Nah, I agree with you on all your points.
>
> Rune

Correcting myself:

In the first point, I think you meant PSD instead of PDF......it is
precisely because the power (spectral) density (W/Hz) is flat for -inf
to +inf, the total power is infinite....PDF has nothing to do with
power/power density 

Partho

in article 1151413634.184613.34120@x69g2000cwx.googlegroups.com, Rune Allnor
at allnor@tele.ntnu.no wrote on 06/27/2006 09:07:

> 
> Ben wrote:
>> 
>> When we measure "pure white noise", we ise a band-limited measuring
>> device (such as a spectrum analyzer), whose pass band is obviously less
>> than the infinite bandwidth of the pure white noise. Upon measurement,
>> the measuring device LPFs the noise to pink noise, which in turn
>> introduces correlation between neighboring noise samples, leaving the
>> output of the actual measuring black box as patently "non-white".
>> Hence, what we measure is "assumed" to be white noise, but this
>> assumption may never be experimentally verified as fact, since the very
>> act of measurement converts it to some sort of colored noise.
...
> 
> I think you are right all along:
> 
...

> Nah, I agree with you on all your points.

one thing i might disagree with is that not all LPFed white noise is "pink"
which requires a specific LPF that is non-trivial to design.  "colored" is
accurate, but unless your LPF slope is -3 dB/octave, it's not pink.

-- 

r b-j                  rbj@audioimagination.com

"Imagination is more important than knowledge."

Ben wrote:
> > I think you are right all along:
> >
> > - Perfect white noise must, if it exists, have a constant PDF
> >   on the interval <-inf, inf>
> > - Hence it has infinite power
> > - Hence its existence is questionable, at best.
> > - White noise is a useful *model* for analysis of *bandlimited *
> >   systems
> > - There s no such thing as a measurement system with a
> >   perfect impulse response
> >
> > Nah, I agree with you on all your points.
> >
> > Rune
>
> Correcting myself:
>
> In the first point, I think you meant PSD instead of PDF......

Yep, I did.

Rune

Rune Allnor wrote:
> Jerry Avins wrote:
>
> Does Kirchoff's laws distinguish between deterministic
> and stichastic systems? That was new to me.
>
> Rune

Hello Rune,

I hope you are having fun at sea or is this a professional trip or
both? I'm planning to go back in a month or two.

When I think about potentials and currents I think about a "smoothed
out" representation. This works fine until we deal with small currents
or potentials. Schottkey worked out shot noise in terms of the
statistics of the flow of small numbers of charges. In the millampere
range it is not much of a concern; however in the picoampere range it
is a real big deal. An amp is 6.25E18 electrons per second.

True the junction law is based on conservation of charge and the loop
law is based on conservation of energy, but we can't instantaneously
add the voltages across two resistors without accounting for the speed
of light and knowing the exact state of the photon field within the
resistors. We have to talk about the ensemble statistics. So we add
averages. Johnson noise arises from the fluctuations in the photon
field within the conductors. This is really a 1-d application of
Planck's blackbody radiation law. A classic example of generating non
white noise is a heated (relative to its surroundings) object. The
colors of light are emitted at differing strengths.

Clay

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

Clay wrote:

   ...

> True the junction law is based on conservation of charge and the loop
> law is based on conservation of energy, but we can't instantaneously
> add the voltages across two resistors without accounting for the speed
> of light and knowing the exact state of the photon field within the
> resistors. We have to talk about the ensemble statistics. So we add
> averages. Johnson noise arises from the fluctuations in the photon
> field within the conductors. This is really a 1-d application of
> Planck's blackbody radiation law. A classic example of generating non
> white noise is a heated (relative to its surroundings) object. The
> colors of light are emitted at differing strengths.

I'm glad you pointed out "relative to its surroundings". That's 
important enough so I wouldn't have used the parentheses. I use a 
burn-out oven that operates at red heat. It has a peephole in the door 
that serves to show when the flask has reached oven temperature. The 
flask appears dark while it is still cooler. It disappears when it 
reaches the temperature of the walls.

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

Wondering what ZPMs are??? Zener P----- M------???? or something else?

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:
> 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