We check this by looking at the expectation

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Unformatted text preview: ing at the expectation ()() ] ,()()[ ( ) ( )] [ The parameter c(i)’s are not generally orthogonal . The only case that they are orthogonal is when the correlation matrix R can be diagonalized as follows: [() ( )] Or in other words, the Fourier vectors are eigenvectors of the correlation matrix. In that special case we have: [() ( )] { 3c) The expectation ,| ( )| - approximates the eigenvalue associated with the Fourier coefficient 3d) () () ,| ( )| - ̂( ) ∑ () [∑ ∑ ∑ () () Problem 4 [∑ () ( )] () ( )] The only terms that are non-zero in the sum are when basis vectors . Pulling the expectatio...
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