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ECE 630: Statistical Communication Theory
Prof. B.-P. Paris
Homework 4
Due: February 23, 2017
a valid inner product for the space of finite-energy functions defined over [0,T]?
Consider subspace of L_{2}(0,T) that consists of signals of the form
where X_{n} may be complex valued.
where K is the constant the knowledgeable investor is seeking and N_{t} is a random process describing the random fluctuations. Specifically, N_{t} is a white, Gaussian process having spectral height . The investor decides to estimate K using the inner product:
where the “best” function g(t) is to be found.
where x_{n} are known and N_{n} are zero mean, iid Gaussian noise samples with variance σ^{2}. The parameters a and b are to be determined. We can think of the solution to this problem as the projection of onto the subspace spanned by a + b
denotes a vector of 1’s. Explain why or why not?