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From: pnachtwey on 9 Feb 2010 20:03
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
From: Chip Eastham on 9 Feb 2010 20:30
On Feb 9, 8:03 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

Hi, Peter:

If a normal distribution doesn't work for you,
and controlling the peaks is important, how
about using a pdf that is the sum of two (or
more) normal density functions (skewed, if
you wish by putting unequal weights under the
two bell curves).

regards, chip

P.S. Note that the sum of the pdf's is not
the pdf of the sum of two normally distributed
random variables (which would again have a
normal distribution).
From: harry on 9 Feb 2010 21:10

"pnachtwey" <pnachtwey(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.

a scaled Poisson like may be what you are looking for, with 0 at 0 and 0 at
25





From: Ray Koopman on 10 Feb 2010 01:34
On Feb 9, 5:03 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

The following pseudocode will give a triangular density on (0,1)
with a peak at c. It scales easily: to get it on (0,t) with a
peak at s, use c = s/t, then multiply the returned value by t.

generate x and y independent uniform(0,1)
if x < c then if c*y > x then return c-x
else return x
else if (1-c)*y > 1-x then return 1-x+c
else return x
From: pnachtwey on 10 Feb 2010 01:50
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.
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