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Guest
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 Posted: Wed Nov 19, 2008 12:08 pm Post subject: Probability expressions of a signal |
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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 |
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Guest
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| Posted: Wed Nov 19, 2008 12:48 pm Post subject: Re: Probability expressions of a signal |
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On Nov 19, 12:08 pm, karl.polyt...@googlemail.com wrote:
| Quote: | 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 fix |
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emre
Guest
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| Posted: Wed Nov 19, 2008 9:38 pm Post subject: Re: Probability expressions of a signal |
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| Quote: | 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. |
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Guest
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| Posted: Thu Nov 20, 2008 8:13 pm Post subject: Re: Probability expressions of a signal |
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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:
| Quote: | 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. |
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Tim Wescott
Guest
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| Posted: Mon Nov 24, 2008 4:18 am Post subject: Re: Probability expressions of a signal |
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On Wed, 19 Nov 2008 04:48:46 -0800, karl.polytech wrote:
| Quote: | On Nov 19, 12:08Â 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 fix
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So 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 |
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