HW7sol - ENEE 630 Homework #7 Solution to 1 Recall that Γ...

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Unformatted text preview: ENEE 630 Homework #7 Solution to 1 Recall that Γ m =- Δ m − 1 P m − 1 where Δ m − 1 = m − 1 summationdisplay k =0 a m − 1 ,k r ( k- m ) We have r ( m ) =- Γ ∗ m P m − 1- m − 1 summationdisplay k =1 a ∗ m − 1 ,k r ( m- k ) or, Γ m =- r ∗ ( m ) P m − 1- 1 P m − 1 m − 1 summationdisplay k =1 a m − 1 ,k r ∗ ( m- k ) We also need, a m,k = a m − 1 ,k + Γ m a ∗ m − 1 ,m − k , k = 0 , 1 ,... ,m P m = P m − 1 (1- | Γ m | 2 ) (a) P = r (0) = 1 Γ 1 =- r ∗ (1) P =- . 8 P 1 = P (1- | Γ 1 | 2 ) = 0 . 36 Γ 2 =- r ∗ (2) P 1- r ∗ (1) P 1 Γ 1 = 1 9 P 2 = P 1 (1- | Γ 2 | 2 ) = 0 . 356 Also, a 22 = Γ 2 a 21 = Γ 1 + Γ 2 Γ ∗ 1 =- . 889 Δ 2 =- . 0444 Γ 3 =- Δ 2 P 2 = 0 . 125 1 (b) See Figure 1.-1 z-1 z-1 z-0.8-0.8 0.111 0.281 0.281 0.111 u[n] Figure 1: P-1 (c) P 3 = P 2 (1- | Γ 3 | 2 ) = 0 . 35. See Figure 2 P m m 1 1 2 3 Figure 2: P-1 Solution to 2 (a) (i) The tap weights of a prediction error filter is a m = parenleftbigg 1- w parenrightbigg...
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This note was uploaded on 10/31/2010 for the course EE 630 taught by Professor Wu during the Spring '10 term at Aarhus Universitet, Aarhus.

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HW7sol - ENEE 630 Homework #7 Solution to 1 Recall that Γ...

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