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Hello,
Per definition a white noise signal has a zero mean value. yet by
definition also , it has a flat power density, i,e. every frequency
including zero has the same power which means it has a DC value, hence
its mean is not equal to zero.
I am confused. any help please?

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On Aug 12, 7:55=A0am, karl bezzoto <karl.bezz...@googlemail.com> wrote:
> Hello,
> Per definition a white noise signal has a zero mean value. yet by
> definition also , it has a flat power density, i,e. every frequency
> including zero has the same power which means it has a DC value, hence
> its mean is not equal to zero.
> I am confused. any help please?



Hi,


There has been a very long discussion on white noise that is not zero
mean on this group.
I will see if I can find the orignal post and link it here.

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On Aug 12, 11:11=A0am, Neu <ikarosi...@hotmail.com> wrote:
> On Aug 12, 7:55=A0am, karl bezzoto <karl.bezz...@googlemail.com> wrote:
>
> > Hello,
> > Per definition a white noise signal has a zero mean value. yet by
> > definition also , it has a flat power density, i,e. every frequency
> > including zero has the same power which means it has a DC value, hence
> > its mean is not equal to zero.
> > I am confused. any help please?
>
> Hi,
>
> There has been a very long discussion on white noise that is not zero
> mean on this group.
> I will see if I can find the orignal post and link it here.



Found it:


http://groups.google.com/group/comp.dsp/browse_thread/thread/177a51d4376130=
18/6b4628b9a0b0b55a?hl=3Den&q=3D


Feel free to contribute :)
hth

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 > > Hello,
 > > Per definition a white noise signal has a zero mean value. yet by
 > > definition also , it has a flat power density, i,e. every
frequency
 > > including zero has the same power which means it has a DC value,
hence
 > > its mean is not equal to zero.
 > > I am confused. any help please?

 Found it:

 http://groups.google.com/group/comp.dsp/browse_thread/thread/177a51d4...


Also note that when you say "including zero has the same power which
means it has a DC value," it not necessarily true. The condition for
WN is that is the *second order * statistics (ie, autocorrelation) is
an impulse function, which has a flat power spectrum density.

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On Aug 12, 4:55 am, karl bezzoto <karl.bezz...@googlemail.com> wrote:
> Hello,
> Per definition a white noise signal has a zero mean value. yet by
> definition also , it has a flat power density, i,e. every frequency
> including zero has the same power which means it has a DC value, hence
> its mean is not equal to zero.
> I am confused. any help please?

[begin hand waving]
In the infinite continuous domain the idealized white noise has a flat
power density, not value. As you look at the power in a smaller and
smaller interval, the power becomes smaller and smaller. At zero
width, a point, the total power in the interval goes to zero for any
finite density.
[end hand waving]

When we have only a finite set of samples, the sample set does not
exactly match the characteristics of the theoretical continuous-
infinite white noise. Larger sample sets usually get you closer.

Dale B. Dalrymple

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On 12 Aug, 16:38, dbd <d...@ieee.org> wrote:
> On Aug 12, 4:55 am, karl bezzoto <karl.bezz...@googlemail.com> wrote:
>
> > Hello,
> > Per definition a white noise signal has a zero mean value. yet by
> > definition also , it has a flat power density, i,e. every frequency
> > including zero has the same power which means it has a DC value, hence
> > its mean is not equal to zero.
> > I am confused. any help please?
>
> [begin hand waving]
> In the infinite continuous domain the idealized white noise has a flat
> power density, not value. As you look at the power in a smaller and
> smaller interval, the power becomes smaller and smaller. At zero
> width, a point, the total power in the interval goes to zero for any
> finite density.
> [end hand waving]
>
> When we have only a finite set of samples, the sample set does not
> exactly match the characteristics of the theoretical continuous-
> infinite white noise. Larger sample sets usually get you closer.
>
> Dale B. Dalrymple

thanks to both of you. i'll study your answers more carefully

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On 12 Aug, 13:55, karl bezzoto <karl.bezz...@googlemail.com> wrote:
> Hello,
> Per definition a white noise signal has a zero mean value. yet by
> definition also , it has a flat power density, i,e. every frequency
> including zero has the same power which means it has a DC value, hence
> its mean is not equal to zero.
> I am confused. any help please?

I'd say that a non-zero mean would cause a Dirac Delta
at f = 0. The zero-mean white noise would have a non-zero
power *denisty* near f = 0, but the contribution to the
power would vanish as the bandwidth vanishes.

Rune

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On Aug 12, 11:38=A0am, dbd <d...@ieee.org> wrote:
> On Aug 12, 4:55 am, karl bezzoto <karl.bezz...@googlemail.com> wrote:
>
> > Hello,
> > Per definition a white noise signal has a zero mean value. yet by
> > definition also , it has a flat power density, i,e. every frequency
> > including zero has the same power which means it has a DC value, hence
> > its mean is not equal to zero.
> > I am confused. any help please?
>
> [begin hand waving]
> In the infinite continuous domain the idealized white noise has a flat
> power density, not value. As you look at the power in a smaller and
> smaller interval, the power becomes smaller and smaller. At zero
> width, a point, the total power in the interval goes to zero for any
> finite density.
> [end hand waving]
>
> When we have only a finite set of samples, the sample set does not
> exactly match the characteristics of the theoretical continuous-
> infinite white noise. Larger sample sets usually get you closer.
>
> Dale B. Dalrymple

So it is similar to statistics with a continuous variable given  pdf
(x) the probability at any individual point is zero?

Don't you just love mathematics  :)

Cheers,
Dave

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Dave wrote:
> On Aug 12, 11:38 am, dbd <d...@ieee.org> wrote:
>> On Aug 12, 4:55 am, karl bezzoto <karl.bezz...@googlemail.com> wrote:
>>
>>> Hello,
>>> Per definition a white noise signal has a zero mean value. yet by
>>> definition also , it has a flat power density, i,e. every frequency
>>> including zero has the same power which means it has a DC value, hence
>>> its mean is not equal to zero.
>>> I am confused. any help please?
>> [begin hand waving]
>> In the infinite continuous domain the idealized white noise has a flat
>> power density, not value. As you look at the power in a smaller and
>> smaller interval, the power becomes smaller and smaller. At zero
>> width, a point, the total power in the interval goes to zero for any
>> finite density.
>> [end hand waving]
>>
>> When we have only a finite set of samples, the sample set does not
>> exactly match the characteristics of the theoretical continuous-
>> infinite white noise. Larger sample sets usually get you closer.
>>
>> Dale B. Dalrymple
> 
> So it is similar to statistics with a continuous variable given  pdf
> (x) the probability at any individual point is zero?
> 
> Don't you just love mathematics  :)

With an infinite number of probability points and a finite sum, what 
would you expect?

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

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On Aug 14, 9:38=A0am, Jerry Avins <j...@ieee.org> responded:


>
> > So it is similar to statistics with a continuous variable given =A0pdf
> > (x) the probability at any individual point is zero?
>
> > Don't you just love mathematics =A0:)

>
> With an infinite number of probability points and a finite sum, what
> would you expect?


A (countably) infinite number of points *can* have probabilities
that sum to 1, but these points *cannot* all have *equal* probability.
The sum is, of course, defined in the sense of a limit (this is the
topic that causes most people to fall asleep in their calculus
classes :-) )  and a sum of the form c + c + c + ... + c does not
converge to a finite value as the number of terms in the sum
increases.  (Sums of the form c + c(1-c) + c(1-c)^2 + ... + c(1-c)^
{n-1}
=3D 1-(1-c)^n do converge to 1 provided that c is in (0, 1] but the
terms
are not equal ....)

For a continuous random variable, the number of possible value is
*uncountably* infinite, and the notion of a *sum* of all such values
is not defined in the above sense; the corresponding notion is that
of an integral or area under the pdf, which we should remember
stands for probability *density* function: it is measured in units
of probability mass per unit length, and we don't get a probability
from the pdf unless we "multiply" by a length or integrate the pdf
over an interval.  The "reason" that the probability that a continuous
variable X equals c is 0 is that the "point" c has zero length (or
width if you prefer) and so multiplying the pdf value by the length
(or doing an integral if you prefer) gives 0; there is no *area* under
the curve above the point of zero width.  In short, a good reason for
loving mathematics is its insistence that c times 0 is 0 for any
real number c (and no, "infinity" is not a real number.....).

Dilip Sarwate

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