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Unformatted text preview: UCLA Dept. of Electrical Engineering EE M214A, Winter 2011 Problem Set 5 Solution February 16, 2011 1. Answer: 2. Answer: 1 3. Answer: 4. Answer: (a) The autocorrelation function is given by: R ( i ) = N 1 summationdisplay n =0 x ( n ) x ( n i ) R (0) = 3 2 + 2 2 + ( 1) 2 + 1 2 = 15 R (1) = 3 2 + 2  1 + 1 1 = 3 R (2) = 3  1 + 2 1 = 1 R (3) = 3 1 = 3 Thus: R ( i ) = [15 , 3 , 1 , 3] For order N = 2, the normal equations can be expressed in matrix form as: 2 R = bracketleftbigg R (0) R (1) R (1) R (0) bracketrightbigg = bracketleftbigg 15 3 3 15 bracketrightbigg r = bracketleftbigg R (1) R (2) bracketrightbigg = bracketleftbigg 3 1 bracketrightbigg a = R 1 r = bracketleftbigg 2 9 1 9 bracketrightbigg G = radicalbig E min H ( z ) = G 1 2 9 z 1 + 1 9 z 2 (b) E min = R (0) 2 summationdisplay k =1 a k R ( k ) (12) = 15 parenleftbigg 2 9 parenrightbigg (3) parenleftbigg 1 9 parenrightbigg ( 1) (11) = 14 . 22 (10) (9) Since LPC assumes an allpole system, the minimum error occurs at the poles of the transfer...
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This note was uploaded on 04/19/2011 for the course EE 214A taught by Professor Alwan during the Winter '11 term at UCLA.
 Winter '11
 ALWAN
 Electrical Engineering

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