[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 22:05:44 -0400
You're right, Lei. I looked up a probability book and the sign is plus.
Thanks for the correction.
Ihsan
On 4/14/06, Lei Luo <leiluo@xxxxxxxxx> wrote:
>
> That's right. (RMS)^2=(RMS1)^2+(RMS2)^2+2*coeff*RMS1*RMS2: where coff is
> the cofferent (-1<coeff<1) between event1 and event2,
>
> Give example here, assume RMS2=RMS1:
> For case coeff=-1, which means event1 and event2 alway in opposite
> direction, then RMS=0
> For case coeff=1, which means event1 and event2 always in same direction,
> then RMS=2*RMS1
> For case coeff=0, which means they are independant, then RMS=sqrt(2)*RMS1;
>
> Ihsan, you may have a typo here: "-2*" should be "+2*",
>
> Regards,
>
>
> Lei
>
> On 4/14/06, Ihsan Erdin <erdinih@xxxxxxxxx> wrote:
> >
> > 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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