本科实验报告课程名称：信号与系统实验姓名：院系：专业：学号：指导教师：周绮敏、史笑兴、李惠忠年月日实验报告课程名称： 信号与系统实验 指导老师： 史笑兴、周绮敏、李惠忠 成绩： 实验名称： 实验一 MATLAB 基本实验 实验类型： 设计型 一、实验目的与要求1、掌握Matlab 的基本使用方法：操作界面、基本语法、基本函数等；2、掌握Matlab 在“信号与系统”课程中的应用： （1）信号的产生与表示；（2）产生基本信号的Matlab 函数； （3）卷积和的计算与表示；（4）离散时间信号的傅立叶变换的计算与表示，部分傅立叶变换的性质验证。

二、实验内容和原理1、P168，实验一，习题 1、2、3、4、5、7 2、P169，实验二，习题 1、1的补充题、2、3 3、P170，实验三，习题 1、2、3三、主要仪器设备带有matlab 的电脑一台四、操作方法和实验步骤4.1 新建文本文档并命名，在文本文档中写matlab 代码，另存为.m 的文件，此时注意名称开头不应为数字，标题中不应出现matlab 自带函数的名称； 4.2打开matlab 程序，运行已保存好的.m 文件，根据提示的错误信息修改代码直至无错误为止，运行代码，记录运行结果。

五、实验数据记录和处理 实验1.1 代码：clear;clf;clc; %Impulse sequence subplot(2,2,1); n=[-10:10]; z=(n==0); stem(n,z);axis([-10,10,-1,2]); title('Impulse sequence'); xlabel('n');ylabel('delta[n]');%Impulse function subplot(2,2,2); t=-10:0.1:10;专业： 姓名： 学号：日期：5.3—5.24 地点：东四420室实验时间： 周 第 节课 签到表编号：y=(t==0);plot(t,y,'r');axis([-10,10,-1,2]);title('Impulse function');xlabel('t');ylabel('\delta(t)');%Step Sequencesubplot(2,2,3);n=[-10:10];z=(n>=0);stem(n,z);axis([-10,10,-1,2]);title('Step sequence');xlabel('n');ylabel('u[n]');%Step functionsubplot(2,2,4);t=-10:0.1:10;y=(t>=0);plot(t,y,'b');axis([-10,10,-1,2]);title('Step function');xlabel('t');ylabel('u(t)');结果：实验1.2代码：%sine wavesubplot(2,2,1);t=-2*pi:pi/20:2*pi;plot(t,sin(t));axis([-2*pi,2*pi,-1.5,1.5]); title('Sine wave');xlabel('t');ylabel('sin(t)');%Triangular wavesubplot(2,2,2);t=-5*pi:pi/100:5*pi;x=sawtooth(t,0.5);plot(t,x);axis([-5*pi,5*pi,-1.5,1.5]); title('Triangular wave'); xlabel('t');ylabel('x');%Sawtooth wavesubplot(2,2,3);t=-5*pi:pi/100:5*pi;z=sawtooth(t,0);plot(t,z);axis([-5*pi,5*pi,-1.5,1.5]); title('Sawtooth wave t=0'); xlabel('t');ylabel('z');subplot(2,2,4);t=-5*pi:pi/100:5*pi;z=sawtooth(t,1);plot(t,z);axis([-5*pi,5*pi,-1.5,1.5]); title('Sawtooth wave t=1'); xlabel('t');ylabel('z');结果：实验1.3代码：clear;clf;clc;%Sinc functiont=-4*pi:pi/20:4*pi;subplot(2,1,1);plot(t,sinc(t));axis([-4*pi,4*pi,-0.5,1.5]);title('Sinc function');grid on;xlabel('t');ylabel('sinc(t)');%Sample functionsubplot(2,1,2);plot(t,sinc(t/pi));axis([-4*pi,4*pi,-0.5,1.5]);title('Sample function');grid on;xlabel('t');ylabel('sa(t)');结果：实验1.4代码：u1=stepseq(0,-5,20);u3=stepseq(5,-5,20);x=u1-u3;n=[-5:20];h=delta(n-5);subplot(3,1,1);stem(n,x);axis([-5,20,0,1.2]);title('x[n]'); xlabel('n');ylabel('x[n]');subplot(3,1,2);stem(n,h);axis([-5,20,0,1.2]);title('h[n]');xlabel('n');ylabel('h[n]');[y,ny]=conv_my(x,n,h,n)subplot(3,1,3);stem(ny,y);axis([-5,20,0,1.2]);title('y[n]');xlabel('n');ylabel('y[n]');结果：实验1.5代码：n=[-10:10];x1=delta(n);x2=delta(n+2);x3=delta(n-4);x4=2*delta(n+2)-delta(n-4);subplot(2,2,1);stem(n,x1);title('x_1[n]=\delta[n]');axis([-10,10,-1,2]);grid on;subplot(2,2,2);stem(n,x2);title('x_2[n]=\delta[n+2]');axis([-10,10,-1,2]);grid on;subplot(2,2,3);stem(n,x3);title('x_3[n]=\delta[n-4]');axis([-10,10,-1,2]);grid on;subplot(2,2,4);stem(n,x4);title('x_4[n]=2*\delta[n+2]-delta[n-4]'); axis([-10,10,-1,2]);grid on;结果：实验1.7代码：clear;clf;clc;n=[-15:15];x1=stepseq(0,-15,15);x2=stepseq(10,-15,15);x=x1-x2;[xe,xo]=evenodd(x);subplot(2,2,1);stem(n,x);title('Step sequence');xlabel('n');ylabel('x[n]');axis([-15.5,15.5,-1.2,2]);subplot(2,2,3);stem(n,xe);axis([-15,15,-1,2]);title('Even part'); xlabel('n');ylabel('xe[n]');axis([-15.5,15.5,-1.2,2]);subplot(2,2,4);stem(n,xo);title('Odd part');xlabel('n');ylabel('xe[n]');axis([-15.5,15,-1.2,1.2]);结果：实验2.1代码：clear;clf;clc;n=[-5:10];nx=[-5:10];nh=[-5:10];h=delta(n-5)*1.0;x=stepseq(0,-5,10)-stepseq(5,-5,10);[y,ny]=conv_m(x,nx,h,nh);subplot(3,1,1);stem(n,x);title('x[n]');xlabel('n');axis([-5,10,0,1.2] );grid on;subplot(3,1,2);stem(n,h);title('h[n]');xlabel('n');axis([-5,10,0,1.2] );grid on;subplot(3,1,3);stem(ny,y);title('y[n]');xlabel('n');axis([-10,20,0,1. 2]);grid on;结果：实验2.1补充题代码：u1=stepseq(5,-10,10);u3=stepseq(-5,-10,10);x=(abs(n)<=5)*1.0;n=[-10:10];nx=[-10:10];nh=[-10:10];h=delta(n+3)-delta(n-3);[y,ny]=conv_m(x,nx,h,nh);subplot(3,1,1);stem(n,x);axis([-10,10,-0.5,1.5]);title('x[n]'); xlabel('n');ylabel('x[n]');subplot(3,1,2);stem(n,h);axis([-10,10,-1.5,1.5]);title('h[n]');xlabel('n');ylabel('h[n]');subplot(3,1,3);stem(ny,y);axis([-20,20,-1.5,1.5]);title('y[n]'); xlabel('n');ylabel('y[n]');结果：实验2.2a 代码：n=-5:20;u1=stepseq(0,-5,20);u2=stepseq(6,-5,20);x=u1-u2;h=n.*x;subplot(3,1,1);stem(n,x);axis([-5,20,0,2]);title('Input Sequence');ylabel('x[n]');subplot(3,1,2);stem(n,h);axis([-5,20,0,6]);title('Impulse Sequence');ylabel('x[n]');[y1,ny]=conv_m(x,n,h,n);subplot(3,1,3);stem(ny,y1);title('Output Sequence');xlabel('n');ylabel('y_1[n]');结果：b 代码：n=-10:20;u1=stepseq(0,-10,20);u2=stepseq(6,-10,20);x=u1-u2;u3=stepseq(-5,-10,20);u4=stepseq(1,-10,20);x1=u3-u4;h=(n+5).*x1;subplot(3,1,1);stem(n,x);axis([-10,20,0,2]);title('Input Sequence');ylabel('x[n]');subplot(3,1,2);stem(n,h);axis([-10,20,0,6]);title('Impulse Response');ylabel('h[n+5]');[y2,ny]=conv_m(x,n,h,n);subplot(3,1,3);stem(ny,y2);title('OutputSequence');xlabel('n');ylabel('y_2[n]');结果：实验2.3代码：n=-5:50;u1=stepseq(0,-5,50);u2=stepseq(10,-5,50);x=u1-u2;h=(0.9).^n.*(n>=0);subplot(3,1,1);stem(n,x);axis([-5,20,-1,2]);title('x[n]'); ylabel('x[n]');subplot(3,1,2);stem(n,h);axis([-5,50,-1,2]);title('h[n]'); ylabel('h[n]');[y,ny]=conv_m(x,n,h,n);subplot(3,1,3);stem(ny,y);axis([-10,70,-2,8]);title('y[n]'); xlabel('n');ylabel('y[n]');结果：实验3.1代码：clear;clc;clf;n=[-20:20];x=stepseq(-5,-20,20)-stepseq(6,-20,20);w1=-2*pi;w2=2*pi;w_step=pi/400;w=w1:w_step:w2;ww=w/pi;xw=spec(x,n,w); %wsubplot(2,2,1);plot(ww,abs(xw));axis([-2,2,0,max(abs(xw))]);grid on; xlabel('w');title('Abs(X)');subplot(2,2,2);plot(ww,angle(xw));axis([-1.2,1.2,-1.2*pi,1.2*pi]); grid on;xlabel('w');title('Phase(X)');subplot(2,2,3);plot(ww,real(xw));axis([-2,2,min(real(xw)),max(real(xw))]);grid on;xlabel('w');title('Real(X)');subplot(2,2,4);plot(ww,imag(xw));axis([-2,2,min(imag(xw)),max(imag(xw))]);grid on;xlabel('w');title('Imag(X)');结果：实验3.2代码：n=0:100;x=cos(pi*n/2);py=exp(j*pi*n/4);y=py.*x;w = -pi : pi/800 : pi;ww=w/pi;xw=spec(x,n,w);yw=spec(y,n,w);subplot(2,2,1);plot(ww,abs(xw));title('Magnitude of X');grid; ylabel('|X|');xlabel('Normalized Freq.(¦Ð rad/s)');axis([ min(ww) , max(ww) , 0, max(abs(xw)) ]);subplot(2,2,2);plot(ww,angle(xw));title('Angle of X');grid; ylabel('Angle(X)');xlabel('Normalized Freq.(¦Ð rad/s)');axis([ min(ww) , max(ww) , -pi, pi ]);subplot(2,2,3);plot(ww,abs(yw));title('Magnitude of Y');grid; ylabel('|Y|');xlabel('Normalized Freq.(¦Ð rad/s)');axis([ min(ww) , max(ww) , 0, max(abs(yw)) ]);subplot(2,2,4);plot(ww,angle(yw));title('Angle of Y');grid; ylabel('Angle(Y)');xlabel('Normalized Freq.(¦Ð rad/s)');axis([ min(ww) , max(ww) , -pi, pi ]);结果：实验3.3代码：n=-5:10;x=sin(pi*n/2);w1=-pi;w2=pi;w_step=pi/800;w=w1:w_step:w2;X=spec(x,n,w);[xe,xo,m]=evenodd2(x,n);clf;XE=spec(xe,m,w);XO=spec(xo,m,w);XR=real(X);XI=imag(X);subplot(3,2,1);plot(w/pi,XR,'r');grid;axis([-1,1,min(XR),max(XR)]); xlabel('Normalized Freq.(\pi rad/sample)');ylabel('Re[X]');title('Real part of X');subplot(3,2,2);plot(w/pi,XI,'r');grid;axis([-1,1,min(XI),max(XI)]); xlabel('Normalized Freq.(\pirad/sample)');ylabel('Im(X)');title('Imaginary part of X');subplot(3,2,3);plot(w/pi,real(XE),'r');grid;axis([-1,1,min(real(XE)),max(real(XE))]);xlabel('Normalized Freq.(\pi rad/sample)');ylabel('XE or Re(XE)');title('DFT of even part-real');subplot(3,2,4);plot(w/pi,imag(XE),'r');grid;axis([-1,1,min(imag(XE)),max(imag(XE))]);xlabel('Normalized Freq.(\pi rad/sample)');ylabel('Im(XE)');title('DFT of even part-Imaginary');subplot(3,2,5);plot(w/pi,real(XO),'r');grid;axis([-1,1,min(real(XO)),max(real(XO))]);xlabel('Normalized Freq.(\pi rad/sample)');ylabel('Re(XO)');title('DFT of oddd part-Real');subplot(3,2,6);plot(w/pi,imag(XO),'r');grid;axis([-1,1,min(imag(XO)),max(imag(XO))]);xlabel('Normalized Freq.(\pi rad/sample)');ylabel('XO/j or Im(XO)');title('DFT of odd part-Imaginary');结果：子函数：1.stepseq.mfunction [x,n]=stepseq(n0,n1,n2)n=n1:n2;x=(n>=n0);函数的功能是产生阶跃函数，其中n1和n2是函数的横坐标边界，n0是跳变点。