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From: Vladimir Vassilevsky on 10 Feb 2010 11:10


pnachtwey wrote:
> Does anybody have a good way of simulating sample jitter?
> I want to beef up my simulations. Normal distribution isn't good
> enough because the distribution isn't skewed and it doesn't allow one
> to have a zero probability at 0 and almost 0 at some point in the
> future like 25 microseconds and then be able to adjust the where the
> peak probability is in between like at 6 microseconds.
>
> Gamma or Beta distributions may work but they required a whole lot of
> calculations which slow down a simulation. Also they are hard to
> scale.
>
> I have seen articles on the topic not specifically about the
> simulation function used, at least not good ones.

Calculate a polynomial using uniformly distributed random number as an
argument. Chose polynomial coefficients so the result would be an
approximation of the desired PDF. A polynomial of the order 3...5 would
be probably good enough for practical purpose. In my experience, the pdf
is not very important; it is mostly the RMS value that matters.

Vladimir Vassilevsky
DSP and Mixed Signal Design Consultant
http://www.abvolt.com
From: rickman on 10 Feb 2010 11:20
On Feb 10, 1:50 am, pnachtwey <pnacht...(a)gmail.com> wrote:
> On Feb 9, 6:10 pm, "harry" <nos...(a)invalid.com> wrote:
>
> > "pnachtwey" <pnacht...(a)gmail.com> wrote in message
>
> >news:07d168e2-a5c1-43d8-ae78-e5f9735a1fd5(a)t31g2000prh.googlegroups.com....
>
> > > Does anybody have a good way of simulating sample jitter?
> > > I want to beef up my simulations.  Normal distribution isn't good
> > > enough because the distribution isn't skewed and it doesn't allow one
> > > to have a zero probability at 0 and almost 0 at some point in the
> > > future like 25 microseconds and then be able to adjust the where the
> > > peak probability is in between like at 6 microseconds.
>
> > > Gamma or Beta distributions may work but they required a whole lot of
> > > calculations which slow down a simulation.  Also they are hard to
> > > scale.
>
> > > I have seen articles on the topic not specifically about the
> > > simulation function used, at least not good ones.
>
> > > Peter Nachtwey
>
> > Depends highly on what your noise source is, or what your channel is.
>
> > If driven by a clock in a microprocessor, it can be modeled as a flat
> > distribution.
>
> Yes,  think if responding to interrupts generated by the on board
> timer of a micro-controller. There will be a distribution of sample
> times after the interrupt.  I doubt is will be flat but more like the
> poisson distribution you mention below.
>
>
>
> > a scaled Poisson like may be what you are looking for, with 0 at 0 and 0 at
> > 25
>
> Poisson has the right look but it isn't continuous.
>
> Peter Nachtwey
>
> I am trying to simulate sample jitter.  A CPU generates interrupts at
> fixed intervals but interrupts may be turned off.  Normally interrupts
> are off for only a short period of time but sometimes they are off
> long than others.


The distribution you are trying to model is not likely to be any of
the standard curves. It will likely be multi-modal with small
distributions around each mode. For each location in the code where
you turn off interrupts for a set time period, you will see a mode in
the data for this time period plus the interrupt response time of the
processor (which is likely a distribution of its own). If the code
has lots of these interrupt disabling code segments which act for
different amounts of time, then it may average out to something like a
normal distribution. But you are also going to have a number of
interrupt responses with interrupts enabled at the time of the
interrupt giving a mode corresponding to the native interrupt response
time of the processor. I expect it may be a bit like time duration of
telephone calls.

http://www.bbc.co.uk/dna/h2g2/A956289 scroll to bottom of page.

A mode for very short calls, a mode for calls a bit longer (faxes) and
the rest tailing off to long times. You case may be even more complex
with multiple longer modes corresponding to the different sections of
code where interrupts are disabled.

Rickfor
From: spudnik on 10 Feb 2010 11:22
very crude, but true!

> The distribution you are trying to model is not likely to be any of
> the standard curves.  It will likely be multi-modal with small
> distributions around each mode.  For each location in the code where
> you turn off interrupts for a set time period, you will see a mode in
> the data for this time period plus the interrupt response time of the
> processor (which is likely a distribution of its own).  If the code
> has lots of these interrupt disabling code segments which act for
> different amounts of time, then it may average out to something like a
> normal distribution.  But you are also going to have a number of
> interrupt responses with interrupts enabled at the time of the
> interrupt giving a mode corresponding to the native interrupt response
> time of the processor.  I expect it may be a bit like time duration of
> telephone calls.
>
> http://www.bbc.co.uk/dna/h2g2/A956289 scroll to bottom of page.
>
> A mode for very short calls, a mode for calls a bit longer (faxes) and
> the rest tailing off to long times.  You case may be even more complex
> with multiple longer modes corresponding to the different sections of
> code where interrupts are disabled.

thus:
doc EEE doesn't want to believe,
that Simon Stevin *defined* _The Decimals_
to have a sole ambiguity:
3.14159999... is the same "real" number as
3.14160000...

it also appears in "Dedikind cuts," I think;
thus, the Surreals!

thus:
I did not follow the meaning of your terms, but
it seems like a good approach, using the mean-value theorem;
however, "the" fixed-point th. is an easy proof in,
what?, analysis texts (but
I'm not allowed to googol that .-)

and, there are probably dozens or hundreds of kinds
of FP theorems; eh?

--les Oeuvres!
http://wlym.com
From: harry on 10 Feb 2010 11:35

"Vladimir Vassilevsky" <nospam(a)nowhere.com> wrote in message
news:Cc6dnUQ_mqH5R-_WnZ2dnUVZ_tqdnZ2d(a)giganews.com...
>


>In my experience, the pdf is not very important; it is mostly the RMS value
>that matters.


agree - It dosent have to match exactly, but generally,

also checkout Erlang queing (a,b and c) may be overkill
"Poisson like" is what you need
wiki "poisson distribution" - has a generator there


>
> Vladimir Vassilevsky
> DSP and Mixed Signal Design Consultant
> http://www.abvolt.com


From: aruzinsky on 10 Feb 2010 11:40
On Feb 9, 7:03 pm, pnachtwey <pnacht...(a)gmail.com> wrote:
> Does anybody have a good way of simulating sample jitter?
> I want to beef up my simulations.  Normal distribution isn't good
> enough because the distribution isn't skewed and it doesn't allow one
> to have a zero probability at 0 and almost 0 at some point in the
> future like 25 microseconds and then be able to adjust the where the
> peak probability is in between like at 6 microseconds.
>
> Gamma or Beta distributions may work but they required a whole lot of
> calculations which slow down a simulation.  Also they are hard to
> scale.
>
> I have seen articles on the topic not specifically about the
> simulation function used, at least not good ones.
>
> Peter Nachtwey

Jitter PSFs are often, if not typically, spatially variant.

Spatial variance can be seen in this example:
http://www.general-cathexis.com/images/DSC00115.png

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