L l 12 3 review smoothed periodogram under general

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Unformatted text preview: iew: smoothed periodogram Under general conditions, the Xc (k - l/n) and Xs (k - l/n) are asymptotically independent and N (0, f (k - l/n)/2). Thus, ^ ^ Ef ( (n) ) f () and Varf ( (n) ) f 2 ()/L. Notice the bias-variance trade off: 1. Our assumption that f is approximately constant on [ - L/(2n), + L/(2n)] becomes worse as L increases, so the difference ^ between f (^(n) ) and f () (the bias) will increase with L. ^ 2. The variance of our estimate, Varf (^(n) ) decreases with L. 4 Other smoothed spect...
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