> ... I assumed "mathematical simplicity" to be
> mutually exclusive to "practical use"!!!
That's not a good assumption. Mathematical simplicity makes many
idealizations suitable for practical calculation. Can you imagine
studying statics without the unreal idealization of "rigid body"?
Jerry
--
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������
Reply by Ben●June 29, 20062006-06-29
I reexamined your response after sending in mine, and realized that the
first statement
> > We now know for sure that "pure white noise" is a hypothetical entity,
is not what you contest, rather my premise that
> > used for mathematical simplicity rather than any practical use.
is what seems whacky since I assumed "mathematical simplicity" to be
mutually exclusive to "practical use"!!!
Partho
>
> > 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."
>
> In short, white noise is a mathematically simple hypothetical
> construction of great practical utility. Does that answer your question?
>
> Perhaps you've studied Strength of Materials. If so, you know how to
> calculate the deflection of a loaded beam. If you remember the
> derivation of the calculation, you'll recall the hidden assumption that
> the beam is undeflected. That assumption comes from the explicit
> assumption that transverse planes through the undeflected beam remain
> parallel throughout the analysis. The analysis yields results accurate
> to a few tenths of a percent at loads that don't cause beam failure.
>
> Jerry
> --
> Engineering is the art of making what you want from things you can get.
> =AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=
> ;-)
>
> There goes my theory in the trash can!!! But, yes no harm in
> hypothesizing half of physics and keeping the other half intact!!!
Hey Ben,
I apologize if I was a bit hard on you.
I reexamine my response and I say to myself, "At least
he's trying to reason things out, and that's a very good
thing."
By all means, bring your thoughts and questions, even the
ill-formed ones, here to comp.dsp, and if the old-farts like
me have a little too much heartburn with something, just ignore us.
There are plenty of folks here who will engage you in a positive
and encouraging way.
--Randy
Reply by Jerry Avins●June 28, 20062006-06-28
Ben wrote:
> So you do not dispute that it actually exists in the universe, do you?
> inspite of the fact that "pure white noise" will need an infinite BW?
The phrasing of your question would be appropriate if thought I believed
that white noise exists. I assume that's a misreading; in any case, I
don't. Your top posting makes it difficult to show my remarks coherently
in context, so I'll quote here:
"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."
In short, white noise is a mathematically simple hypothetical
construction of great practical utility. Does that answer your question?
Perhaps you've studied Strength of Materials. If so, you know how to
calculate the deflection of a loaded beam. If you remember the
derivation of the calculation, you'll recall the hidden assumption that
the beam is undeflected. That assumption comes from the explicit
assumption that transverse planes through the undeflected beam remain
parallel throughout the analysis. The analysis yields results accurate
to a few tenths of a percent at loads that don't cause beam failure.
Jerry
--
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������
> 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.
�����������������������������������������������������������������������
Reply by Ben●June 28, 20062006-06-28
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
Reply by Ben●June 28, 20062006-06-28
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
Reply by Ben●June 28, 20062006-06-28
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
Reply by Randy Yates●June 28, 20062006-06-28
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