实验三

Laboratory Exercise 3 (2 class hours)

Z-TRANSFORM

Project 3.1Computation of Impulse and Step Responses of LTI Systems

Program P3_1 is given below as an example for calculating the impulse and step response of the filter through using the impz and stepz function.

% Program P3_1 Compute the impulse and step response N

= 40;

num = [2.2403 2.4908 2.2403]; den = [1 -

0.4 0.75]; h = impz(num,den,N); %

Impulse response s = stepz(num,den,N); %

Step response

% Plot the

response subplot(2,1,1)

stem(h);

xlabel('Time index n'); ylabel('Amplitude');

title('Impulse Response'); grid;

subplot(2,1,2) stem(s);

xlabel('Time index n'); ylabel('Amplitude');

title('Step Response'); grid; Q3.1

z-domain manipulation

Use z-transform and inverse z-transform to find out the impulse and step response of the filter, and compare them with the results obtained by using the impz and stepz function. You may probably use the syms, ztrans, iztrans associate

结论：由图可知,用“impz”和“z-trans”得到的脉冲响应和频率响应相同。

Project 3.2 Calculate the Output of Cascaded LTI Systems

Program P3_2 given below is for calculating the output of a cascaded filter.

% Program P3_2 Cascade Realization

clear clc

N = 30; x =

rand(1,N);

% coefficients of the two cascaded filters

num1 = [0.3 -0.2 0.4];den1 = [1 0.9 0.8];

num2 = [0.2 -0.5 0.3];den2 = [1 0.7 0.85]; %

output y1 obtained by filter function y1 =

filter(num1,den1,filter(num2,den2,x)); %

output y2 obtained by z-domain method

< your codes >

% Plot and compare the outputs obtained by the above two methods h1 = stem(y1,'marker','x','color','b'); hold on

h2 = stem(y2,'marker','s','color','r');

legend([h1,h2],'filter','z-transform');

xlabel('n'); ylabel('Amplitude'); grid

on;

Q3.2Complete the codes in the above program and plot the outputs here.

在“your codes”处写的代码如下：

得到如下图形：

Project 3.3 Pole-zero Plot and Partial Fraction Expansion.

H(z) z2 z z1 6

1 zz 1 1 z6 2z

2

Q3.3 Use zplane to plot the pole-zero plot, assuming that you cannot get the roots of the denominator manually. Code:

B=[0,1,-1]; A=[1,1,-

6]; zplane(B,A);

图形如右：

Q3.4 Use residuez tofind out the partial fraction expansion of H(z).

运行代码后，在工作区可找到r,p,k的值：