离散时间系统的时域分析

实 验 报 告专业班级 电科* 姓名 * 学号 20084836* 实验日期 2010 年 11 月 29 日实验名称 离散时间系统的时域分析 一、 实验目的：在时域中，离散时间系统对输入信号或者延迟信号进行简单运算处理，生成具有所需特性的输出信号，通过MATLAB仿真一些简单的离散时间系统，并研究它们的时域特性。本次实验目的是验证系统的线性与时不变性，以及计算线性时不变系统的冲激响应，用系统的冲激响应与给定的有限长输入序列进行卷积得到有限冲激响应系统的输出序列。二、实验内容：1.线性系统的特性验证程序如下：% Program P2_3% Generate the input sequencesclf;n = 0:40;a = 4;b = -6;x1 = cos(2*pi*0.2*n);x2 = cos(2*pi*0.8*n);x = a*x1 + b*x2;num = 2.2403 2.4908 2.2403;den = 1 -0.4 0.75;ic = 0 0; % Set zero initial conditionsy1 = filter(num,den,x1,ic); % Compute the output y1ny2 = filter(num,den,x2,ic); % Compute the output y2ny = filter(num,den,x,ic); % Compute the output ynyt = a*y1 + b*y2; d = y - yt; % Compute the difference output dn% Plot the outputs and the difference signalsubplot(3,1,1)stem(n,y);ylabel(Amplitude);title(Output Due to Weighted Input: a cdot x_1n + b cdot x_2n);subplot(3,1,2)stem(n,yt);ylabel(Amplitude);title(Weighted Output: a cdot y_1n + b cdot y_2n);subplot(3,1,3)stem(n,d);xlabel(Time index n);ylabel(Amplitude);title(Difference Signal)；运行结果：2.时不变系统的特性验证(1)D=15 w1=0.1*2pi w2=0.4*2pi程序如下：% Program P2_4-1% Generate the input sequencesclf;n = 0:40; D = 15;a = 3.0;b = -2;x = a*cos(2*pi*0.1*n) + b*cos(2*pi*0.4*n);xd = zeros(1,D) x;num = 2.2403 2.4908 2.2403;den = 1 -0.4 0.75;ic = 0 0; % Set initial conditions% Compute the output yny = filter(num,den,x,ic);% Compute the output ydnyd = filter(num,den,xd,ic);% Compute the difference output dnd = y - yd(1+D:41+D);% Plot the outputssubplot(3,1,1)stem(n,y);ylabel(Amplitude); title(Output yn); grid;subplot(3,1,2)stem(n,yd(1:41);ylabel(Amplitude);title(Output due to Delayed Input xn -, num2str(D),); grid;subplot(3,1,3)stem(n,d);xlabel(Time index n); ylabel(Amplitude);title(Difference Signal); grid;运行结果：(2)D=10 w1=0.2*2pi w2=0.8*2pi程序如下：% Program P2_4-1% Generate the input sequencesclf;n = 0:40; D = 10;a = 3.0;b = -2;x = a*cos(2*pi*0.2*n) + b*cos(2*pi*0.8*n);xd = zeros(1,D) x;num = 2.2403 2.4908 2.2403;den = 1 -0.4 0.75;ic = 0 0; % Set initial conditions% Compute the output yny = filter(num,den,x,ic);% Compute the output ydnyd = filter(num,den,xd,ic);% Compute the difference output dnd = y - yd(1+D:41+D);% Plot the outputssubplot(3,1,1)stem(n,y);ylabel(Amplitude); title(Output yn); grid;subplot(3,1,2)stem(n,yd(1:41);ylabel(Amplitude);title(Output due to Delayed Input xn -, num2str(D),); grid;subplot(3,1,3)stem(n,d);xlabel(Time index n); ylabel(Amplitude);title(Difference Signal); grid;运行结果：3.计算线性时不变系统的冲激响应程序如下：% Program P2_5% Compute the impulse response yclf;N = 45;num = 0.9 -0.45 0.35 0.002;den = 1 0.71 -0.46 -0.62;y = impz(num,den,N);% Plot the impulse responsestem(y);xlabel(Time index n); ylabel(Amplitude);title(Impulse Response); grid;运行结果：4.通过卷积得到有限冲激响应系统的输出序列程序如下：% Program P2_7clf;h = 3 2 1 -2 1 0 -4 0 3; % impulse responsex = 1 -2 3 -4 3 2 1; % input sequencey = conv(h,x);n = 0:14;subplot(2,1,1);stem(n,y);xlabel(Time index n); ylabel(Amplitude);title(Output Obtained by Convolution); grid;x1 = x zeros(1,8);y1 = filter(h,1,x1);subplot(2,1,2);stem(n,y1);xlabel(Time index