{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

20111eeM214A_1_ps511_sol

# 20111eeM214A_1_ps511_sol - UCLA Dept of Electrical...

This preview shows pages 1–4. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

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 all-pole system, the minimum error occurs at the poles of the transfer...
View Full Document

{[ snackBarMessage ]}

### Page1 / 7

20111eeM214A_1_ps511_sol - UCLA Dept of Electrical...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online