[SI-LIST] Re: How do two Random (Gaussian) Jitter specs add?
- From: "Ihsan Erdin" <erdinih@xxxxxxxxx>
- To: "Lei Luo" <leiluo@xxxxxxxxx>
- Date: Fri, 14 Apr 2006 12:04:20 -0400
All right, we're getting deeper into this. You touched a good point, Lei.
The underlying assumption in RSS is that the events are independent. If
they're dependent things get a bit complicated. For the sake of simplicity
let's take two dependent events. In this case you need to know the
covariance matrix between them. Then the variance of these two events
becomes: var(event1)+var(event2)-2*cov(event1,event2). In the case of two
independent events, this equation collapses to our earlier simple RSS. Once
you find the variance the sigma is simply the square root of it. Any
comments objections, corrections?
Regards
Ihsan
On 4/14/06, Lei Luo <leiluo@xxxxxxxxx> wrote:
>
> Hi, Tom and Ihsan:
>
> Suppose we have two RMS: rms_1 and rms_2. If they are totally independant,
> then we can do RMS add, just as Ihsan did. If they are dependant on each
> other, with a coefficient, then I dont' think you can do this RMS add. In
> the worst case, if they are totally dependant, I suggest linear add them. I
> maybe wrong, please comment on this. Thanks,
>
> Lei
>
> On 4/14/06, Ihsan Erdin <erdinih@xxxxxxxxx> wrote:
>
> > Hi Tom,
> I don't call myself an SI expert but I guess I can answer your question.
> You're correct in your assumtion that RMS values don't add linearly. A
> vector addition applies instead, which is also known as root-sum-square
> (RSS), i.e. sqrt( (rms_1)^2+(rms_2)^2+...+(rms_n)^2 )
>
> Regards.
>
> Ihsan
>
> On 4/14/06, tom_cip_11551 <tom_cip_11551@xxxxxxxxxxx> wrote:
> >
> > Hi to sll signal integrity experts.
> >
> > I am just a little rusty on "probability and random variables".
> >
> > Lets say that I had a system with two or more elements that
> > generated Gaussian distribution or, random jitter, or random jitter.
> > Random jitter tends to be specifed in terms of the standard
> > deviation of the distribution. Each generator would therefore have
> > a "sigma", which is also an RMS value. If I knew the sigma of each
> > of the distributions coming from the generators, then I could
> > convert these sigma values to a peak to peak number by arbitrarily
> > assigning a desired bit error rate. The peak to peak values, as far
> > as I know, will add, linearly.
> >
> > However, if I wanted to stay in the statistical world, how could I
> > add the two sigma values for the two jitter generators? In my way of
> > thinking, they can not add linearly (sigma 1 plus sigma 2). Is this
> > wrong?
> >
> > Thank You
> > Tom
> >
> >
> >
> >
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> --
> Lei Luo, Ph.D.
> Senior Member of Technical Staff
> Rambus Inc.
> Chapel Hill, NC
>
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