Re: A question about Covariance??
- From: "Srikar" <srikarshetty@xxxxxxxxx>
- Date: 31 May 2006 01:38:13 -0700
VijaKhara wrote:
Dear members,
For two Real Random Process X(t) and Y(t), the cross-covariance is Mean
of ((X(t)-MeanX(t))(Y(t)-MeanY(t)).
I learn that people calculate the correlation of two Random Process to
determine how similar two processes are. I am wondering what is the
target of calculating the covariance? If we want to find out the
similarity of two process, correlation is enough, why we need
covariance?
One more thing, correlation is for determine the similarity of two
processes, what is the target of Auto-correlation?
Thanks a lot.
Regards
VijaKhara,
when dealing with more than one random process, it should be obvious
that it would be nice to be able to have a number that could quickly
give us an idea of how similar the processes are. To do this, we use
the covariance, which is analogous to the variance of a single
variable.
A measure of how much the deviations of two or more variables or
processes match.For two processes, X and Y if they are not closely
related then the covariance will be small, and if they are similar then
the covariance will be large. Two processes are "closely related" if
their distribution spreads are almost equal and they are around the
same, or a very slightly different, mean.
Correlation of two variables provides us with a measure of how the two
variables affect one another.
A measure of how much one random variable depends upon the
other.This measure of association between the variables will provide us
with a clue as to how well the value of one variable can be predicted
from the value of the other. The correlation is equal to the average
of the product of two random variables.
with Autocorrelation {Rxx(t)} we can find the energy of the signal.
Energy of the signal = Rxx(0);
.
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