上海交通大学：《数字信号处理 Digital Signal Processing（B）》教学资源_Handouts_ch7_Digital Filter Realization

Introduction To Digital Signal Processing 主讲：张君 上气大学

Introduction To Digital Signal Processing 主讲：张君

IIR-Direct form Introduction to Digital Signal Processing--Digital Filter Realization H(z)= N(2)_b+bz1+b2z2 The main feature of this D(2) a+412+a2z2 realization A single adder All the b-multiplier terms ya=-diya-1-42y-2+bo*+bx-1+bx2 are feeding forward The a-multiplier terms are feeding back 2~1 -a w1() 7 V2(n b2 -a w2(n) 上游充通大￥

Introduction to Digital Signal Processing—— Digital Filter Realization IIR-Direct form 2 2 1 0 1 2 2 1 0 1 ( ) ( ) ( )           a a z a z b b z b z D z N z H z n   1 n1  2 n2  0 n  1 n1  2 n2 y a y a y b x b x b x The main feature of this realization •A single adder •All the b-multiplier terms are feeding forward •The a-multiplier terms are feeding back

IIR -Direct form Introduction to Digital Signal Processing--Digital Filter Realization 'o(0m)=x(m) 1wo(m)=-a1M(m)-a21w2(m)+boYo(m)+b1(m)+b2'2(n) y(n)=wo(n) '2(n+1)=1() 1w2(1+1)=1(n) (n+1)=yo(m %(n+1)=1o(0m) for each input x do: Vo=X Wo=-a1W1-a2W2+bovo+b1V1+b2V2 y=Wo V2=V1,W2=W1 V1=Vo W1=Wo 上游充通大￥

Introduction to Digital Signal Processing—— Digital Filter Realization IIR -Direct form

IIR -Direct form NG U Introduction to Digital Signal Processing--Digital Filter Realization H(z)= N(2)_b+bz1+b2z2+…+b,z1 D(a ）a+az1+az2++aw -M x(n) y(n) yn=-ayn-1-a2yn-2-..-amyn-M +box+bx1+b2x2++bLxn-L ,(0n+1)=-10m) i=0.12,…,L %(n+1)=1w(n-i) i=01.2.…,M 上游充通大￥

Introduction to Digital Signal Processing—— Digital Filter Realization IIR -Direct form M M L L a a z a z a z b b z b z b z D z N z H z                   2 2 1 0 1 2 2 1 0 1 ( ) ( ) ( ) n n n L n L n n n M n M b x b x b x b x y a y a y a y                   0 1 1 2 2 1 1 2 2

IIR -Direct form Introduction to Digital Signal Processing--Digital Filter Realization N() 2-3z-1+4z-3 H()= D(2)1+0.2=1-0.3z2+0.524 yn=0.2ym-+0.3ym-2-0.5ym-4+2x,-3xm-1+4xm-3 x(n) y(n) Vo Wo 2-1 -0. 0.3 W -0.5 W 上游充通大

Introduction to Digital Signal Processing—— Digital Filter Realization IIR -Direct form

IIR-canonical form (Direct form II) RS Introduction to Digital Signal Processing--Digital Filter Realization yn =boxn +bxn-1+b2xn-2 +(-ayn-1-a2yn-2) e- gNertgge x(n) y(n) Vo(n wo(n) 7 wj(n) 21 b2 w2(n) N(Z) 1/D(Z 上游充通大

Introduction to Digital Signal Processing—— Digital Filter Realization IIR-canonical form (Direct form II) ( ) n  0 n  1 n1  2 n2   1 n1  2 n2 y b x b x b x a y a y ( ) ( ) 1 ( ) 1 ( ) ( ) ( ) ( ) N z D z D z N z D z N z H z     

IIR-canonical form (Direct form II) Introduction to Digital Signal Processing--Digital Filter Realization H(z)= N(a)_ 1 ·N(z) D(2 D(2 x(n) w(n) w(n) bo y(n) Wo(n) Wo(n) 21 W() 21 21 W2( W2() 1/D(Z) N(Z 上游充通大

Introduction to Digital Signal Processing—— Digital Filter Realization IIR-canonical form (Direct form II) ( ) ( ) 1 ( ) ( ) ( ) N z D z D z N z H z   

IIR-canonical form (Direct form II) Introduction to Digital Signal Processing--Digital Filter Realization w(n)=x(n)-a1w(n-1)-a2w(n-2) Y(n)=bow(n)+b1w(n-1)+b2w(n-2) 21 W(Z)=X(Z)-azW(Z)-a2 zW(Z) Y(Z)=boW(Z)+b1zW(z)+b2z W(Z) Y(z)=(bo+bjz-+bzz 2)W(z)=N(z)W(z) Y(z)=N(2)W(2)= N(②X(2) D(z) 上游充通大

Introduction to Digital Signal Processing—— Digital Filter Realization IIR-canonical form (Direct form II)

IIR-canonical form (Direct form II) Introduction to Digital Signal Processing--Digital Filter Realization Y(z)=N(Z)W(Z) 1+a121+a222+a323++awzM)W(z)=X(2) W)-X) Y(2)=(bo+b2-1+b22-2+b323+..+bL2)w(z) D(Z) W(2)=X(2)-(ajz+a222+a3z3+..+avz-M)W(z) Y(2)=(bo+b2+b222+b323+...+b2)W(2) w(n)=x(m)-a1w(n-1)-a2wn-2)-a3w(n-3)-…-aMw(n-M) y(n)=bow(n)+bw(n-1)+b2w(n-2)+b3w(n-3)++bIw(n-L) 上洛充通大警

Introduction to Digital Signal Processing—— Digital Filter Realization IIR-canonical form (Direct form II)

IIR-canonical form (Direct form II) Introduction to Digital Signal Processing--Digital Filter Realization Wo(n)=x(n)-aw(n)-a2W2(n)-a3W3(n)-...-amWm(n) y(n)=bowo(n)+bW(n)+b2W2(n)+b3W3(n)+...+bLWL(n) w:(n+1)=w+(n) i=K,K-1,…,2,1 x(n) w() bo y(n) y() -a1 b1 for each input x do: W1() Wo=X-a1W1-a2W2--aMWM y=bowo+biW1+b2w2++bLW Z-1 wi(n+1)=w-1(n)I=K,K-1,,2,1 -a2 b2 21 by 上浒充通大

Introduction to Digital Signal Processing—— Digital Filter Realization IIR-canonical form (Direct form II)