Block Diagram Representation (Direct Form I) M l=∑an-+∑b,n-1→ml=∑a[n-+网 k=1 x[n] bo yn] →y[n] by a x[n-1] y[n-1] x[n-2] y[n-2] bM aN-1 x[n-(M-1)]止 y[n-(-1)] x[n-M] bM y[n-N] 12
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] x[n-(M-1)] . . . . . . 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 = = = − + − + z −1 z −1 + z −1 + a1 aN−1 aN y[n] y[n-1] y[n-2] y[n-N] y[n] y[n-(N-1)] . . . . . . (Direct Form I)
Block Diagram Representation (Direct Form I) M [m=∑bx[n-k] y[=∑ay[n-k]+[n k=0 k=1 Implementing zeros o v(n] Implementing poles x[n] yn] 21 a x[n-1] y[n-1] x[n-2] y[n-2] an-1 x[n-M] bM an y[n-N] 13
Implementing zeros 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 Implementing poles
Block Diagram Representation (Direct Form I) m=∑bhn-k] m之an-k]+W k=0 Implementing zeros v[n] Implementing poles x[n] yn Y(2) H271L-之a- k=1 Ha发8 Y(2-H()H.(a) 1=之a4z k=1 14
Implementing zeros 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] 0 [ ] [ ] M k k v n b x n k = = − 1 [ ] [ ] [ ] N k k y n a y n k v n = = − + Implementing poles 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− = = = − 0 1 2 1 ( ) ( ) ( ) ( ) ( ) 1 M k k k N k k k b z Y z H z H z H z X z a z − = − = = − = = 1 0 [ ] [ ] [ ] N M k k k k y n a y n k b x n k = = = − + −
Block Diagram Representation (Direct Form I) How many Adders? N+M How many multipliers? N+M+1 How many delays? N+M x[n] bo v n y[n] 21 by a x[n-1] y[n-1] x[n-2] [n-2] an-1 1 15 x[n-M] bM an y[n-N]
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) M n=∑bx[n-k] y[=∑aJLn-k]+v[网 k=0 k=1 x[n] bo v(n] y(n] a x[n-1] yn-1] V(②) M Y(a) X(2) H,(a)=∑bz H2(2)= N k=0 1-∑az V(2) k=1 x[n-M] y[n-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] 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 = = − = M k k k H z b z 0 1 ( ) = − − = N k k k a z H z 1 2 1 1 ( )