Block Diagram Representation(Direct Form I M N =∑-+∑m=的]=∑am+ k=0 k=1 ∑bxn-k k=0 Xin ∠ xn-1] yn-1 xn-2] yIn-2 M-1 aN-1 ∠ xin- yn-N
12 Block Diagram Representation (Direct Form I) v[n] + z −1 z −1 + z −1 + b0 b1 bM−1 bM x[n] x[n-1] x[n-2] x[n-M] + z −1 z −1 + z −1 + a1 aN−1 aN y[n] y[n-1] y[n-2] y[n-N] 1 [ ] [ ] [ ] N k k y n a y n k v n = = − + 1 0 [ ] [ ] [ ] = = = − + − N M k k k k y n a y n k b x n k 0 [ ] [ ] M k k v n b x n k = = −
Block Diagram Representation (Direct Form I 1l=∑bn-kym=∑an-刷]+叫 k=0 k=1 xX y C x[n2] n-2 H H1() X(z) ∑b-26 k=0 ∑a=k
13 + z −1 z −1 + z −1 + b0 b1 bM−1 bM x[n] x[n-1] x[n-2] x[n-M] + z −1 z −1 + z −1 + a1 aN−1 aN y[n] y[n-1] y[n-2] y[n-N] Block Diagram Representation (Direct Form I) v[n] 0 [ ] [ ] M k k v n b x n k = = − 1 [ ] [ ] [ ] N k k y n a y n k v n = = − + 1 0 ( ) ( ) ( ) M k k k V z H z b z X z − = = = 2 1 ( ) 1 ( ) ( ) 1 N k k k Y z H z V z a z − = = = −
Block Diagram Representation (Direct Form I Implementing yIn Implementing zeros pe oles xin v[nl yIn x[n-1 yn-1 M ∑b=-6 H()=H1(2H()=∑b k=0 k=0 ∑
1 [ ] [ ] [ ] N k k y n a y n k v n = = − + 0 [ ] [ ] M k k v n b x n k = = − 14 + z −1 z −1 + z −1 + b0 b1 bM−1 bM x[n] x[n-1] x[n-2] x[n-M] + z −1 z −1 + z −1 + a1 aN−1 aN y[n] y[n-1] y[n-2] y[n-N] Block Diagram Representation (Direct Form I) v[n] = − = M k k k H z b z 0 1 ( ) = − − = N k k k a z H z 1 2 1 1 ( ) Implementing zeros Implementing poles 0 1 2 0 1 1 1 ( ) ( ) ( ) 1 1 M k M k k k k N N k k k k k k k b z H z H z H z b z a z a z − − = = − − = = = = = − −
Block Diagram Representation (Direct Form D) How many Adders? n+M How many multipliers+M+1 How many delays? N+M xn vIn C x xn-2] vn-2 M x[n-M yln-NI
15 Block Diagram Representation (Direct Form I) v[n] How many Adders? How many multipliers? How many delays? + z −1 z −1 + z −1 + b0 b1 bM−1 bM x[n] x[n-1] x[n-2] x[n-M] + z −1 z −1 + z −1 + a1 aN−1 aN y[n] y[n-1] y[n-2] y[n-N] N N N+M +M +M+1
Block Diagram Representation (Direct Form I n=∑ n k] ∑ayn-k]+vl k=0 k=1 xX n y 2 H2(z) X(=) H()=∑b=4 k=0 1-∑a4= k yn-N 16
16 + z −1 z −1 + z −1 + b0 b1 bM−1 bM x[n] x[n-1] x[n-2] x[n-M] + z −1 z −1 + z −1 + a1 aN−1 aN y[n] y[n-1] y[n-2] y[n-N] Block Diagram Representation (Direct Form I) v[n] = − = M k k k H z b z 0 1 ( ) = − − = N k k k a z H z 1 2 1 1 ( ) 0 [ ] [ ] M k k v n b x n k = = − 1 [ ] [ ] [ ] N k k y n a y n k v n = = − + ( ( ) ) X V z z = ( ) ( ) Y z V z =