If you can provide more structure, then we might be able to do
something. For example, are all the x[i]'s and e[i]'s independent of
each other? If you assume some correlation structure among either the
x[i]'s or the e[i]'s, we might be able to make some progress.
Otherwise, in a sample of N, all I see right now are N equations and 2N
unknowns.
hth. spencer graves
Xao Ping wrote:
Dear All:
Suppose that I have a sample Y. Suppose also that it is known that Y=X+E
where X is considered as a signal and E as noise. The PDFs of X and E
are known: F(y, theta) and
G(e, xi). Parameters theta and xi are also a priori known. Given all
this knowledge,
is that possible to estimate signal X? Just to be precise, I need to
substitute each data point in Y by the predicted Y' in such a way as it
would be, in a sense, closer to X than in the original sample Y.
Thank you
Xao
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