第06章系統(tǒng)實(shí)現(xiàn)結(jié)構(gòu)

CHAPTER6structuresfordiscrete-timesystem

6.1signalflowgraphrepresentationoflinearconstant-coefficientdifferenceequations

signalflowgraphrepresentationoflinearconstant-coefficientdifferenceequations

basicstructuresforIIRsystem

directforms

cascadeforms

parallelforms6.2.4.latticestructure

basicstructuresforFIRsystem

directforms

cascadeforms

structuresforlinear-phaseFIRsystem6.2.4.latticestructure

Figure6.8

EXAMPLE

z-1

Figure6.9

節(jié)點(diǎn)：源、阱、網(wǎng)絡(luò)支路：常數(shù)、z-1、1、-1

節(jié)點(diǎn)值=所有輸入支路之和

x[n]

w1[n]

w2[n]

w3[n] 2

z-1

-1 3

w4[n]

6

w5[n]z-1

y[n]

轉(zhuǎn)置：所有支路反向

輸入輸出交換輸入輸出關(guān)系不變

轉(zhuǎn)置形式

z-1

basicstructuresforIIRsystem

directforms

directI

N M

y[n]=aky[n-k]+bkx[n-k]

k=1 k=0

M N

w1[n]

y[n]

w3[n] 2

z-1

-1 3

x[n]

w[n]=bkx[n-k],y[n]=w[n]+aky[n-k]

k=0 k=1

M

w2[n]

w4[n]

6

w5[n]z-1

H(z)=

bkz-kk=0

N

N

1-akz-k

M

=bkz

k=0

-k 1 1-akz-k

=H1(z)H2(z)

k=1 k=1

W(z)=X(z)H1(z),Y(z)=W(z)H2(z),

M N

w[n]=bkx[n-k],y[n]=w[n]+aky[n-k]

k=0 k=1

2 3

y[n]=a[k]y[n-k]+b[k]x[n-k]

k=1 k=0

直接形式的

C語(yǔ)言實(shí)現(xiàn)

while(!eof(in_file))

Figure6.14

優(yōu)點(diǎn)：簡(jiǎn)單；缺點(diǎn)：延遲多；對(duì)字長(zhǎng)敏感；調(diào)整零極點(diǎn)不便

{ for(k=3;k>0;k++)x[k]=x[k-1];

x[0]=getc(in_file)-128;for(k=2;k>0;k++)

y[k]=y[k-1];for(k=0,y[0]=0;k<=3;k++)

y[0]+=b[k]*x[k];for(k=1;k<=2;k++)

y[0]+=a[k]*y[k]putc(out_file,y[0]+128);

}

//M=3

/N=2

directII（典范型）

M

bkz-k

N

H(z)=k=0 =H1(z)H2(z)=H2(z)H1(z)

1-akz-k

k=1

x[n]

N M

w[n]=x[n]+akw[n-k]，y[n]=bkw[n-k]

k=1 k=0

w[n] b0

z-1

y[n]

where:H2(z)=

1

N

1-akz-kk=1

M

,H1(z)=bkz-k

k=0

a1

z-1

a2

z-1 b1

z-1 b2

W(z)=X(z)H2(z)

Y(z)=W(z)H1(z)

N

\w[n]=x[n]+akw[n-k]

k=1

aN-1

aN

z-1

z-1

bM-1

bM

M

y[n]=bkw[n-k]

k=0

6.2.2cascadeforms

M

bkz-k

[MAX(M,N)+1]/2 [MAX(M,N)+1]/2

1+b

z-1+b

z-2

N

H(z)=k=0 =

1-akz-k

k=1

k=1

Hk(z)=b0

k=1

1k 2k

1-a1kz-1-a2kz-2

[MAX(M,N)+1]/2

b

+bz-1+b

z-2

=

k=1

0k 1k 2k

1-a1kz-1-a2kz-2

Figure6.15

優(yōu)點(diǎn)：延遲少一半

6.2.3parallelforms

M

bkz-k

M-N

[N+1]2

g+g

z-1

H()z=

k=0

=Ckz-k+ ok 1k

Figure6.18

優(yōu)點(diǎn)：可尋找因有限字長(zhǎng)效應(yīng)造成的誤差最小的實(shí)數(shù)零點(diǎn)極點(diǎn)配對(duì)和級(jí)聯(lián)順序；

易于調(diào)整零點(diǎn)和極點(diǎn)；

可用一個(gè)二階環(huán)時(shí)分復(fù)用缺點(diǎn)：不如并行快

1-akz-kk=1

N

=1

k=0

k 1-a1kz-1-a2kz-2

C0

x[n]

α11

z-1

γ01

γ11

y[n]

α21

α1[(N+1)/2]

z-1

γ0[(N+1)/2]

z-1

γ1[(N+1)/2]

優(yōu)點(diǎn)：由有限字長(zhǎng)效應(yīng)造成的總誤差較小；易于調(diào)整極點(diǎn)；

硬件實(shí)現(xiàn)快缺點(diǎn)：不能調(diào)整零點(diǎn)

α2[(N+1)/2]

z-1

Figure6.20

6.2.4.補(bǔ)充格型網(wǎng)絡(luò)

EXAMPLE

basicstructuresforFIRsystem

directforms

M M

H(z)=h(k)z-k,y(n)=h(k)x(n-k)

k=0 k=0

x[n]

-1/3

1/3

-1

H(z)=

-1/2

1/2

-z-1

1

-1/4

1/4

-z-1 -z

y[n]

1+13z-1+5z-2+1z-3

24 8 3

優(yōu)點(diǎn)：對(duì)有限字長(zhǎng)不敏感

Figure6.31

3

y[n]=h[k]x[n-k]

k=0

直接形式的

C語(yǔ)言實(shí)現(xiàn)

cascadeforms

[M+1]

M 2

[M+1]2

while(!eof(in_file))

H()z=h(k)-zk=h[0] (1+b1kz-1+b2kz-2)= (b0k'+b1k'z-1+b2k'z-2)

{ for(k=3;k>0;k++)x[k]=x[k-1];

x[0]=getc(in_file)-128;for(k=0,y[0]=0;k<=3;k++)

y[0]+=h[k]*x[k];putc(out_file,y[0]+128);

}

//M=3

k=0

k=1

k=1

Figure6.33

structuresforlinear-phaseFIRsystem

1Miseven

M

y[n]=h[k]x[n-k]

k=0

M/2-1 M

=h[k]x[n-k]+h[M/2]x[n-M/2]+h[k]x[n-k]

k=0 k=M/2+1

M/2-1 M/2-1

=h[k]x[n-k]+h[M/2]x[n-M/2]+h[M-k]x[n-M+k]

k=0 k=0

M/2-1

= h[k](x[n-k]–x[n-M+k])+h[M/2]x[n-M/2]

k=0

Figure6.34

2.Misodd:

M

y[n]=h[k]x[n-k]

k=0

(M-1)/2 M

=h[k]x[n-k]+h[k]x[n-k]

k=0 k=(M+1)/2

(M-1)/2 (M-1)/2

=h[k]x[n-k]+h[M-k]x[n-M+k]

k=0 k=0

(M-1)/2

= h[k](x[n-k]–x[n-M+k])

k=0

Figure6.35

優(yōu)點(diǎn)：乘法次數(shù)減少一半

補(bǔ)充格型網(wǎng)絡(luò) 小結(jié)

x[n]

1/4

1/2

1/3

1/4

1/2

1