华南理工大学信号及系统实验报告.docVIP

Experiment Export Name: Student No: Institute: Dec 26, 2011 Experiment Purposes 1. Be familiar with the software Environment and Programming flow in MATLAB5.3. 2. Learn how to draw the signal waveform and determine the signal properties. 3. Calculate the convolution, frequency response and system output by using the functions: conv, freqz, freqs and filter. Experiment Contents 实验项目一：MATLAB编程基础及典型实例 ①? ? 画出离散时间正弦信号并确定基波周期(注：pi? 表示圆周率)1? ? x1[n]=sin(pi*4/4)*cos(pi*n/4)2? ? x2[n]=cos(pi*n/4)*cos(pi*n/4)3? ? x3[n]=sin(pi*n/4)*cos(pi*n/8) program for matlabn=0:31;x1=sin(pi*n/4).*cos(pi*n/4);x2=cos(pi*n/4).*cos(pi*n/4);x3=sin(pi*n/4).*cos(pi*n/8);subplot(3,1,1);stem(n,x1);title(x1);subplot(3,1,2);stem(n,x2);title(x2);subplot(3,1,3);stem(n,x3);title(x3);grid on;? Conclusion: These signals is periodic, the first and second signal’s period are 4. The third signal’s period is 16.?②? ?? 离散时间系统性质：离散时间系统往往是用几个性质来表征，如线性、时不变性、稳定性、因果性及可逆性等。MATLAB可用来构成一些反例证明某些性质不满足。(a) 系统y[n]=sin((pi/2)x[n])不是线性的。利用信号x1[n]=δ[n]和x2=2δ[n]来证明该系统不满足线性性质。(b) 系统 y[n]=x[n]+x[n+1]不是因果的。利用信号x[n]=u[n]证明它。定义向量x和y分别代表在-5=n=9上的输入和在-6=n=9上的输出。Program for matlab 1.4(a) n=[0:20]; x1=[1 zeros(1,20)]; x2=2*x1; x=x1+x2; y1=sin((pi/2)*x1); y2=sin((pi/2)*x2); y=sin((pi/2)*x); figure(1),stem(n,y1) figure(2),stem(n,y2) figure(3),stem(n,y) 1.4(b) x1=[zeros(1,5) ones(1,10)]; x2=[zeros(1,4) ones(1,11)]; y=x1+x2; n1=[-5:9]; n2=[-5:9]; figure(1),stem(n1,x1) figure(2),stem(n2,y) Conclusion: y[n]=sin((pi/2)x[n]) is not linear and y[n]=x[n]+x[n+1] is not cuasal and the result is shown in the chart above.? eq \o\ac(○,3)卷积计算：有限长信? QUOTE ? QUOTE ??和? QUOTE ? QUOTE ? ??(1)? ? 用解析方法计算y[n]=x[n]*h[n](2)? ? 用conv计算y。步骤：a. 定义0≤n≤5区间上的向量x?b. 定义0≤n≤5区间上的向量hc. 用y=conv(x,h)计算yd. 构造y的标号向量nye. 用stem(ny,y)画出结果f. 验证此结果与解析导出的结果是否一致？Program for matlab?N=6; M=6; L=N+M-1; x=[1,1,1,1,1,1]; h=[0,1,2,3,4,5]; y=conv(x,h); nx=0:N-1; nh=0:M-1; ny=0:L-1; stem(ny,y