武汉大学数字信号实验四

姓名:全权 学号：2013302530120 班级:信安4班 日期：2015年5月8日

实验4 数字滤波器结构

实验内容：

6.1 REALIZATION OF FIR TRANSFER FUNCTIONS(FIR传递函数 ) Project 6.1 Cascade 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 same length for calling tf2zp. num = input('Numerator coefficient vector = '); den = input('Denominator coefficient vector = '); [b,a] = eqtflength(num,den); % make lengths equal [z,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：

B?s?b1sn?1??bn?1s?bnZ?s?(s?z1)(s?z2)H(s)??n?1 ?H(s)??kA?s?a1s??am?1s?amP?s?(s?p1)(s?p2)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联形式

(s?zn)

(s?pm)(s?z1)(s?z2)H(s)?k(s?p1)(s?p2)Lb?bz?1?bz?2(s?zn)2k ?H(z)?g?0k1k?1?2k?1(s?pm)1?a1kz?b2kz转换后的系数矩阵保存在sos中 )

Answers: Q6.1

By 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):_h[0]=2 β11=3 ββ

22=2 β13=1 β23=0.5 H1(z)=2（1+3z-1

21=2 β12=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 these factors is given below:

Q6.2

H1(z) is a _不是一个线性的_________ -phase transfer function.

By running Program P6_1 with num = [6 31 74 102 74 31 6] and den = [1] we arrive at the following second-order factors: h[0]=6 β11=15/6 β13=2/3 β23=1/3 _____ 21=1 β12=2 β22=3 β

The block-diagram of the cascade realization obtained from these 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:

6.2 REALIZATION OF IIR TRANSFER FUNCTIONS(IIR传递函数) Project 6.2 Cascade Realization Answers: Q6.3

By running Program P6_1 with num = [3 8 12 7 2 -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 0.2500 1.0000 1.0000 1.0000 1.0000 0.50000 0.5000 _P=3/16 β11=-1/3 β21=0 α11=1/2 α21=0 β12=2 β22=2 α12=1/2 α22=1/4 β13=1 β23

=1 α13=1/2 α23=1/2

The block-diagram of the cascade realization obtained from these factors is given below:

Q6.4

By 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 0.2500 1.0000 1.0000 2.0000 1.0000 0.6667 0.3333 1.0000 1.0000 0.5000 1.0000 1.0000 0.3333 _P=1/18 β11

=3 β21=2 α11=1/2 α21=1/4 β12=1 β22=2 α12=2/3 α22=1/3 β13=1 β23=1/2 α13=1 α23=1/3

The block-diagram of the cascade realization obtained from these factors is given below:

A copy of Program P6_2 is given below:

% Program P6_2

% Parallel Form Realizations of an IIR Transfer

num = input( 'Numerator coefficient vector = ' );

den = input( 'Denominator coefficient vector = ' );

[r1,p1,k1] = residuez(num,den);

[r2,p2,k2] = residue(num,den);

disp('Parallel Form I')

disp('Residues are');disp(r1);

disp('Poles are at');disp(p1);

disp('Constant value');disp(k1);

disp('Parallel Form II')

disp('Residues are');disp(r2);

disp('Poles are at');disp(p2);

disp('Constant value');disp(k2);

Project 6.3 Parallel Realization（并联实现） Answers:

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