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Unformatted text preview: where the x i are zeromean and jointly Gaussian with E[x i x j ]= µ ij and ⌡ ⌠ T S n (t) S m (t) dt = ρ nm . Assume that the S i (t) are linearly independent. a) Compute K x (t,u). b) Is K x (t,u) positive definite? Explain your answer. c) Find a matrix H whose eigenvalues are precisely the nonzero eigenvalues of K x (t,u). Determine an expression for the elements of H in terms of µ ij and ρ nm . Hint: let λ ≠0 and let φ (t) = ∑ i=1 n b i S i (t) Introduce the vector notation b = b 1 b 2 . . . b N Show that if φ (t) is an eigenfunction of K x (.,.) with eigenvalue λ , then λ b = H b...
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This note was uploaded on 06/04/2010 for the course EE 8581 taught by Professor Staff during the Spring '08 term at Minnesota.
 Spring '08
 Staff

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