Folks, It has been a while since i took my course in Probability of theory and i would appreciate any help from you. I am looking to have the symbolic expression of the expectation E and Variance V of the signal Y, where: Y=x1+x2 and x1= cst1(a)+gaussian white noise x2=cst2(a)+gaussian white noise where cst1/cst2(a) returns a real value depending on the value of a ["a" is a parameter uncorrelarated to the signal x1, x2, Y] Thank You
Probability expressions of a signal
Started by ●November 19, 2008
Reply by ●November 19, 20082008-11-19
On Nov 19, 12:08�pm, karl.polyt...@googlemail.com wrote:> Folks, > It has been a while since i took my course in Probability of theory > and i would appreciate any help from you. I am looking to have the > symbolic expression of the expectation �E and Variance V of the signal > Y, where: > Y=x1+x2 and > x1= cst1(a)+gaussian white noise > x2=cst2(a)+gaussian white noise > where cst1/cst2(a) returns a real value depending on the value of a > ["a" is a parameter uncorrelarated to the signal x1, x2, Y] > > Thank YouGuys, forgot to add that E(cst1)=E(Cst2), and Var(Cst1)=Var(Cst2) and both are known and fix
Reply by ●November 19, 20082008-11-19
>Folks, >It has been a while since i took my course in Probability of theory >and i would appreciate any help from you. I am looking to have the >symbolic expression of the expectation E and Variance V of the signal >Y, where: >Y=x1+x2 and >x1= cst1(a)+gaussian white noise >x2=cst2(a)+gaussian white noise >where cst1/cst2(a) returns a real value depending on the value of a >["a" is a parameter uncorrelarated to the signal x1, x2, Y] > >Thank You >Maybe you can use these steps to get your answer: 1) Expectation is linear: E[W+Z] = E[W] + E[Z]. 2) Variance is linear if the inputs are independent: V[W+Z] = V[W] + V[Z], given W,Z independent. (W and Z are independent if they are gaussian and uncorrelated, i.e. E[W Z] = E[W] E[Z].) This may be the case for the gaussian white noise you described above, but make sure it is close to truth before you use that property.
Reply by ●November 20, 20082008-11-20
Cheers for the hints. they were so useful and sufficient to find my way through On Nov 19, 3:38�pm, "emre" <egu...@ece.neu.edu> wrote:> >Folks, > >It has been a while since i took my course in Probability of theory > >and i would appreciate any help from you. I am looking to have the > >symbolic expression of the expectation �E and Variance V of the signal > >Y, where: > >Y=x1+x2 and > >x1= cst1(a)+gaussian white noise > >x2=cst2(a)+gaussian white noise > >where cst1/cst2(a) returns a real value depending on the value of a > >["a" is a parameter uncorrelarated to the signal x1, x2, Y] > > >Thank You > > Maybe you can use these steps to get your answer: > > 1) Expectation is linear: �E[W+Z] = E[W] + E[Z]. > 2) Variance is linear if the inputs are independent: �V[W+Z] = V[W] + > V[Z], given W,Z independent. (W and Z are independent if they are gaussian > and uncorrelated, i.e. E[W Z] = E[W] E[Z].) �This may be the case for the > gaussian white noise you described above, but make sure it is close to > truth before you use that property.
Reply by ●November 23, 20082008-11-23
On Wed, 19 Nov 2008 04:48:46 -0800, karl.polytech wrote:> On Nov 19, 12:08 pm, karl.polyt...@googlemail.com wrote: >> Folks, >> It has been a while since i took my course in Probability of theory and >> i would appreciate any help from you. I am looking to have the symbolic >> expression of the expectation E and Variance V of the signal Y, where: >> Y=x1+x2 and >> x1= cst1(a)+gaussian white noise >> x2=cst2(a)+gaussian white noise >> where cst1/cst2(a) returns a real value depending on the value of a >> ["a" is a parameter uncorrelarated to the signal x1, x2, Y] >> >> Thank You > > Guys, > forgot to add that E(cst1)=E(Cst2), and Var(Cst1)=Var(Cst2) and both are > known and fixSo you are saying that cst1(a) is a random variable with a variance and a mean, and cst2(a) is defined such that cst1(a)/cst2(a) = f(a), where f(a) is some unstated function of a that returns a real number? Then without having some very interesting constraints on f(a) I don't think you can make your claim about the mean and variance of cst2 being equal to cst1, and you are supplying a woefully insufficient set of information for solving the problem. Clarify, please. -- Tim Wescott Wescott Design Services http://www.wescottdesign.com Do you need to implement control loops in software? "Applied Control Theory for Embedded Systems" gives you just what it says. See details at http://www.wescottdesign.com/actfes/actfes.html