连续时间信号的数字处理河南工业大学版.doc

实 验 报 告专业班级 姓名 学号 实验日期 实验名称 连续时间信号的数字处理 一、实验目的：1、连续信号抽样为离散时间信号在时域和频域的效果。2、模拟滤波器的设计。二、实验内容：1、时域中的抽样过程连续正弦信号xa(t)的抽样。% Program P5_1% Illustration of the Sampling Process % in the Time-Domainclf;t = 0:0.0005:1;f = 13;xa = cos(2*pi*f*t);subplot(2,1,1)plot(t,xa);gridxlabel(Time, msec);ylabel(Amplitude);title(Continuous-time signal x_a(t);axis(0 1 -1.2 1.2)subplot(2,1,2);T = 0.1;n = 0:T:1;xs = cos(2*pi*f*n);k = 0:length(n)-1;stem(k,xs);grid;xlabel(Time index n);ylabel(Amplitude);title(Discrete-time signal xn);axis(0 (length(n)-1) -1.2 1.2)；运行结果：将正弦信号频率改为3HZ。运行结果： 将正弦信号频率改为7HZ。运行结果：由图可知，在正弦信号3种不同频率下相应的等效离散时间信号间没有差别。因为xs=cos(2fn), xs(f=13)=cos(0.6n); xs(f=3)=cos(0.6n); xs(f=7)=cos(0.6n);xs的表达式相同，故等效离散时间信号相同。2、时域中的混叠效果（1）、从P5.1所产生的xn中产生重构的信号ya(t)。% Program P5_2% Illustration of Aliasing Effect in the Time-Domain% Program adapted from Kra94 with permission from% The Mathworks, Inc., Natick, MA.clf;T = 0.1;f = 13;n = (0:T:1);xs = cos(2*pi*f*n);t = linspace(-0.5,1.5,500);ya = sinc(1/T)*t(:,ones(size(n) - (1/T)*n(:,ones(size(t)*xs;plot(n,xs,o,t,ya);grid;xlabel(Time, msec);ylabel(Amplitude);title(Reconstructed continuous-time signal y_a(t);axis(0 1 -1.2 1.2);运行结果：（2）、在程序P5.2中，t的范围-0.5至1.5，时间增量的值为2/（500-1）=0.004008。在图中，t的范围是0至1。将图中t的范围改成-0.5至1.5，% Program P5_2% Illustration of Aliasing Effect in the Time-Domain% Program adapted from Kra94 with permission from% The Mathworks, Inc., Natick, MA.clf;T = 0.1;f = 13;n = (0:T:1);xs = cos(2*pi*f*n);t = linspace(-0.5,1.5,500);ya = sinc(1/T)*t(:,ones(size(n) - (1/T)*n(:,ones(size(t)*xs;plot(n,xs,o,t,ya);grid;xlabel(Time, msec);ylabel(Amplitude);title(Reconstructed continuous-time signal y_a(t);axis(-0.5 1.5 -1.2 1.2);运行结果：这种改变后产生的曲线在时间轴0至1上逼近重构的连续时间信号ya(t),在这范围外差别大。？（3）、恢复原始信号显示范围并通过分别改变正弦信号的频率到3HZ和7HZ，重复程序P5.2改变正弦信号的频率到3HZ改变正弦信号的频率到7HZ由图可以看出，相应等效离散时间信号与1中连续正弦信号xa(t)的抽样得到的离散时间信号没有差别。？3、频域中抽样的效果% Program P5_3% Illustration of the Aliasing Effect % in the Frequency-Domainclf;t = 0:0.005:10;xa = 2*t.*exp(-t);%xa = 2*exp(-pi*t.2);% I add myself for teaching.subplot(2,2,1)plot(t,xa);gridxlabel(Time, msec);ylabel(Amplitude);title(Continuous-time signal x_a(t);subplot(2,2,2)wa = 0:10/511:10;ha = freqs(2,1 2 1,wa);plot(wa/(2*pi),abs(ha);grid;xlabel(Frequency, kHz);ylabel(Amplitude);title(|X_a(jOmega)|);axis(0 5/pi 0 2);subplot(2,2,3)T = 1;n = 0:T:10;xs = 2*n.*exp(-n);%xs = 2*exp(-pi*n.2);% I add myself for teaching.k = 0:length(n)-1;stem(k,xs);grid;xlabel(Time index n);ylabel(Amplitude);title(Discrete-time signal xn);subplot(2,2,4)wd = 0:pi/255:pi;hd = freqz(xs,1,wd);plot(wd/(T*pi), T*abs(hd);grid;xlabel(Frequency, kHz);ylabel(Amplitude);title(|X(ejomega)|);axis(0 1/T 0 2)运行结果：将xa(t)改为xa(t)=e-t2运行结果：4、模拟低通滤波器（1）、巴特沃兹低通滤波器的设计% Program P5_4% Design of Analog Lowpass Filter clf;Fp = 3500;Fs = 4500;Wp = 2*pi*Fp; Ws = 2*pi*Fs;N, Wn = buttord(Wp, Ws, 0.5, 30,s);b,a = butter(N, Wn, s);wa = 0:(3*Ws)/511:3*Ws;h = freqs(b,a,wa);plot(wa/(2*pi), 20*log10(abs(h);gridxlabel(Frequency, Hz);ylabel(Gain, dB);title(Gain response);axis(0 3*Fs -60 5);在程序P5