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Unformatted text preview: the k th transform coefficient , is given by the eigenvalue of the R matrix. Assume that the KL transform matrix is constructed according to decreasing eigenvalue magnitude. In other words, . 2 Denote the (i,j) element of a unitary matrix A as . Let denote the transform of obtained when transform matrix A is used. For an autocorrelation matrix as given above, the variance of is: The above summation can be used to compute the transform coefficient variances for any transform by using appropriate values for . Let , m = 1, … , N . where have been arranged in decreasing order. Note that gives the fraction of energy contained in the first m coefficients. • For N = 16, plot versus m for KLT, DCT, and DFT with ρ =0.95. Comment on the resulting plot. • For N = 16, plot log( of KLT – of DCT ) versus m with ρ =0.5, 0.9, 0.95, and 0.99. Comment on the resulting plot. (If you use MATLAB, you can use the command semilogy instead of taking logarithm of .)...
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- Spring '11
- Variance, Probability theory, Singular value decomposition, KL transform, John Villasenor