[SI-LIST] Re: Bounded vs Unbounded jitter (was : Jitter transfer vs. accumulation)

Good plan. This thread does seem to have wandered across a lot of =
territory.=20

One other point about "randomness": When we refer to noise or jitter as =
being "random," that usually conjures up two attributes:

* Having a normal PDF

* AND/or having a broad spread of energy in the spectrum, from dc to =
whatever the bandwidth of the system is.

These are separate concepts and one should not be assumed from the =
presence of the other. You can have signals that have a broad, =
noisy-looking spectrum, but whose PDF does not resemble a normal PDF. =
Conversely you can have jitter or noise that has a normal PDF but a =
bounded spectrum.      =20

Art=20

-----Original Message-----
From: si-list-bounce@xxxxxxxxxxxxx [mailto:si-list-bounce@xxxxxxxxxxxxx] =
On Behalf Of Chris Cheng
Sent: Monday, March 26, 2007 1:24 PM
To: si-list@xxxxxxxxxxxxx
Subject: [SI-LIST] Bounded vs Unbounded jitter (was : Jitter transfer =
vs. accumulation)

Art,
I like your 700 ft tall adult. :-D
In an effort to focus the original message to bandwidth trade-offs in =
=3D
PLL, I propose starting this bounded vs. unbounded jitter discussion in =
=3D
this thread instead.
Thanks in advanced,
Chris

-----Original Message-----
From: si-list-bounce@xxxxxxxxxxxxx
[mailto:si-list-bounce@xxxxxxxxxxxxx]On Behalf Of art_porter@xxxxxxxxxxx
Sent: Monday, March 26, 2007 11:36 AM
To: steven@xxxxxxxxxxxxxxxxxxxx; si-list@xxxxxxxxxxxxx
Subject: [SI-LIST] Re: Jitter transfer vs. accumulation


Here is a thought experiment that helps me think about "random" jitter, =
=3D
=3D3D
which I first encountered when thinking about noise in the ancient days =
=3D
=3D3D
when most digital hardware was so slow we didn't have to worry about =
=3D3D
jitter.=3D3D20

Could the TIE of a transition ever reach 1000 years? If you argue that =
=3D
=3D3D
it could, postulate a condition under which it could do so. (If the PDF =
=3D
=3D3D
is truly normal and unbounded, then of course it could.)=3D3D20

Or think about some other randomly distributed parameter, such as =3D3D
heights of people. As you look at a larger and larger sample of =3D3D
individuals, the PDF gets more and more normal looking. But has there =
=3D
=3D3D
ever been a 0.0005-inch tall adult human being, or a 700-foot tall =3D3D
adult? The normal distribution works fine as a mathematical insight into =
=3D
=3D3D
physical processes such as jitter or noise, as long as you don't force =
=3D
=3D3D
your thinking out of some normal range of bounds, such as the mass that =
=3D
=3D3D
can be supported by a skeleton and musculature, or the height to which =
=3D
=3D3D
the heart can pump blood.=3D3D20

The central limit theorem reminds us that many phenomena appear Gaussian =
=3D
=3D3D
only because they are an accumulation of the effects of a large number =
=3D
=3D3D
of non-random processes. I suspect the same is true of most jitter in =
=3D
=3D3D
the real world.=3D3D20

Art Porter=3D3D20
Agilent Technologies     =3D3D20

-----Original Message-----
From: si-list-bounce@xxxxxxxxxxxxx [mailto:si-list-bounce@xxxxxxxxxxxxx] =
=3D
=3D3D
On Behalf Of Steven Kan
Sent: Monday, March 26, 2007 11:56 AM
To: si-list@xxxxxxxxxxxxx
Subject: [SI-LIST] Re: Jitter transfer vs. accumulation

> From: "Alfred P. Neves" <al.neves@xxxxxxxxxxx>
> Subject: [SI-LIST] Re: Jitter transfer vs. accumulation
> Date: Sat, 24 Mar 2007 09:48:38 -0700
>
> This estimator, peak-peak jitter, is not a good estimator of
> the process since it continues to increase since the process is =3D3D
Gaussian
> and collecting more samples digs deeper into the tails of the
> distribution.    The process is by definition unbounded.
                   ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

IANAE, but I've been thinking about this for awhile now. Though our =
=3D3D
finite=3D3D20
samples may be a "best fit" with the Gaussian, can we really say that =
=3D
=3D3D
any=3D3D20
process is truly unbounded when applied to real-world phenomena that =
=3D3D
occur=3D3D20
in real-world products? If I apply the constraint that I need to examine =
=3D
=3D3D
a=3D3D20
given process over the life of the product (or the life of the user or =
=3D
=3D3D
the=3D3D20
life of the Earth), does that then put bounds the process(es) and =3D
the=3D3D20
resulting statistics?

I can see the argument from the math side, e.g. "unbounded 'by =3D3D
definition'",=3D3D20
but do the 'definitions' include practical constraints?

My empirical gold-bar ratio is still zero.=3D3D20

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