武汉大学数字信号实验四

1、word实验4 数字滤波器结构实验内容：6.1REALIZATION OF FIR TRANSFER FUNCTIONS(FIR传递函数 )Project 6.1Cascade Realization串联实现A copy of Program P6_1 is given below:% Program P6_1A % Conversion of a rational transfer function% to its factored form. % MODIFIED to make the numerator and denominator coefficient vectors % the

2、 same length for calling tf2zp. num = input(Numerator coefficient vector = ); den = input(Denominator coefficient vector = );b,a = eqtflength(num,den);% make lengths equalz,p,k = tf2zp(b,a);sos = zp2sos(z,p,k)指导说明：P6_1程序中， 1.函数tf2zp将系统传递函数的形式从多项式变换成零、极点因式项阶乘形式，即：2.函数zp2sos将系统传递函数由零、极点因式项阶乘形式变换成二阶因子级

3、联形式转换后的系数矩阵保存在sos中 )Answers:Q6.1By running Program P6_1 with num = 2 10 23 34 31 16 4 and den = 1 we arrive at the following second-order factors(二阶因式项):_h0=2 11=3 21=2 12=1 22=2 13=1 23=0.5 H1(z)=21+3z-1+2z-2(1+z-1+2z-2)(1+z-1+0.5z-2)The block-diagram(计算方框图) of the cascade realization obtained from

4、 these factors is given below: H1(z) is a _不是一个线性的_ -phase transfer function.Q6.2By running Program P6_1 with num = 6 31 74 102 74 31 6 and den = 1 we arrive at the following second-order factors: h0=6 11=15/6 21=1 12=2 22=3 13=2/3 23=1/3 _The block-diagram of the cascade realization obtained from t

5、hese factors is given below: H2(z) is a _线性_-phase transfer function.The block-diagram of the cascade realization of H2(z) with only 4 multipliers is shown below:6.2REALIZATION OF IIR TRANSFER FUNCTIONS(IIR传递函数)Project 6.2Cascade RealizationAnswers:Q6.3By running Program P6_1 with num = 3 8 12 7 2 -

6、2 and den = 16 24 24 14 5 5 we arrive at the following second-order factors:_sos= 0.1875 -0.0625 0 1.0000 0.5000 0 1.0000 2.0000 2.0000 1.0000 0.5000 0.25001.0000 1.0000 1.0000 1.0000 0.50000 0.5000_P=3/16 11=-1/3 21=0 11=1/2 21=0 12=2 22=2 12=1/2 22=1/4 13=1 23=1 13=1/2 23=1/2The block-diagram of t

7、he cascade realization obtained from these factors is given below: Q6.4By running Program P6_1 with num = 2 10 23 34 31 16 4 and den = 36 78 87 59 26 7 1 we arrive at the following second-order factors:_sos= 0.0556 -0.1667 0.1111 1.0000 0.5000 0.25001.0000 1.0000 2.0000 1.0000 0.6667 0.33331.0000 1.

8、0000 0.5000 1.0000 1.0000 0.3333_P=1/18 11=3 21=2 11=1/2 21=1/4 12=1 22=2 12=2/3 22=1/3 13=1 23=1/2 13=1 23=1/3The block-diagram of the cascade realization obtained from these factors is given below: A copy of Program P6_2 is given below:%ProgramP6_2%ParallelFormRealizationsofanIIRTransfernum=input(

9、 Numeratorcoefficientvector= );den=input( Denominatorcoefficientvector= );r1,p1,k1=residuez(num,den);r2,p2,k2=residue(num,den);disp(ParallelFormI)disp(Residuesare);disp(r1);disp(Polesareat);disp(p1);disp(Constantvalue);disp(k1);disp(ParallelFormII)disp(Residuesare);disp(r2);disp(Polesareat);disp(p2)

10、;disp(Constantvalue);disp(k2);Project 6.3Parallel Realization并联实现Answers:Q6.5By running Program P6_2 with num = 3 8 12 7 2 -2 and den = 16 24 24 14 5 5 we arrive at the partial-fraction(局部分式) expansion of H1(z) in z1 given by:_0=-2 01=2.3438 11=0 11=0.5 21=0 02=-0.8438 12=-1.0312 12=0.5 22=0.5 03=0.

11、6876 13=2.3437_13=0.5 23=0.25 _and the partial-fraction expansion of H1(z) in z given by:_ 0=0.1875 11=-1.1719 21=0 11=0.5 21=0 12=-0.6094 22=0.4219 12=0.5 22=0.5 13=2 23=-0.1718_13=0.5 23=0.25_(指导说明： 请在MatLab帮助中的Index标签页搜索residue forms. See partial fraction expansion，在search标签页中搜索residue 查看函数功能。 1.

12、函数residue在多项式系数形式与局部分式形式之间互相转换，即：如果存在多重极点，那么局部分式形式为：)The block-diagram of the parallel-form I realization of H1(z) is thus as indicated below: The block-diagram of the parallel-form II realization of H1(z) is thus as indicated below: Q6.6By running Program P6_2 with num = 2 10 23 34 31 16 4 and den

13、= 36 78 87 59 26 7 1 we arrive at the partial-fraction expansion of H2(z) in z1 given by:_0=4 01=-1.1905 11=-0.1587 11=1 21=0.3333 02=-1.1111 12=-1.7778 12=0.6667 22=0.3333 03=-1.6429 13=-4.2143_13=0.5 23=0.25 _and the partial-fraction expansion of H2(z) in z given by:_ 0=0.0.556 11=1.0317 21=0.3968 11=1 21=0.3333 12=2.5185 22=0.3704 12=0.6667 22=0.3333 13=-3.3929