基于Matlab的数字信号处理课程设计课程报告

基于Matlab的数字信号处理课程设计一、课程设计目的：1．熟悉Matlab运行环境，熟练使用Matlab语言进行编程，进行数字信号处理。2．全面复习数字信号课程所学理论知识，巩固所学知识重点和难点，将理论与实践很好地结合起来。3．提高综合运用所学知识独立分析和解决问题的能力；二、MATLAB简介MATLAB是功能强大的科学及计算软件，它不但具有以矩阵计算为基础的强大数学计算和分析功能，而且还具有丰富的可视化图形表现功能和方便的程序设计能力。MATLAB的应用领域极为广泛，除了数学计算和分析外，还被广泛地应用于自动控制、系统仿真、数字信号处理、图形图像分析、数理统计、人工智能、虚拟现实技术、通信工程、金融系统等领域，因此，MATLAB是面向21世纪的计算机程序设计及科学计算语言。三、MATLAB的主要组成部分MATLAB系统包括5个主要部分：（1）开发环境MATLAB开发环境由一组工具和组件组成，这些工具是图形化的用户界面，包括MATLAB桌面和命令窗口、命令历史窗口、帮助信息浏览器、文件和搜索路径浏览器。（2）MATLAB数学函数库MATLAB集成了丰富的数学函数库，其强大的计算能力覆盖了从基本函数（如求和、正弦、余弦和复数运算等）到高级函数（如矩阵求逆、矩阵特征值、贝塞尔函数和快速傅立叶变换等）的范围。（3）MATLAB语言MATLAB语言是一种以矩阵运算为基础的高级语言，包括控制流的描述、函数、数据结构、输入输出及面向对象的编程环境，既可以编制快速使用小程序，也可以编制大型复杂的应用程序。（4）图形功能MATLAB提供了功能强大的图形系统，既可以用高级命令完成二维和三维数据的可视化、图像处理、动画和图形表达等功能，也可以通过使用图形句柄完成复杂的图形功能，实现对所有图形对象的操作。（5）应用程序接口（API）MATLAB还提供了应用程序接口库函数，允许用户使用C或FORTRAN语言编写程序与MATLAB连接，功能包括与MATLAB的动态连接、调用MATLAB作为运算引擎、读写MAT文件等。MATLAB的广泛应用促进了其本身功能的迅速发展，以特定领域的应用为主要目的的应用程序——工具箱的数量和内容在不断增多。四、利用Matlab熟悉画图（设计1）1、设计内容：能够利用Matlab熟悉地画图，内容包括：X、Y坐标轴上的label，每幅图上的title，绘画多条曲线时的legend，对图形进行适当的标注等。（1）在一副图上画出多幅小图；（2）画出一组二维图形；（3）画出一组三维图形；（4）画出复数的实部与虚部。1.实验结果：（1）、在一副图上画出多幅小图；-4-2024-1-0.500.51-1-0.500.5101020304050-4-20240510152025-4-2024-0.500.5（2）、画出一组二维图形；01234567-3-2-10123xy多条曲线绘制y=1*sin(x)y=2*sin(x)y=3*sin(x)（3）、画出一组三维图形；-505-505-2-1012xz=sin2(x)/(3*y-2)yz（4）、画出复数的实部与虚部；0.20.40.60.813021060240902701203001503301800（5）、完成对一个源程序进行详细注释。（见程序）%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%能够利用Matlab熟悉地画图，内容包括：X、Y坐标轴上的label，%每幅图上的title，绘画多条曲线时的legend，对图形进行适当的标注等。%（1）在一副图上画出多幅小图；（2）画出一组二维图形；%（3）画出一组三维图形；（4）画出复数的实部与虚部。%（5）完成对一个源程序进行详细注释。%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%clear;clc;x=linspace(-pi,pi,200);%定义x轴坐标y1=sin(x);%函数1y2=cos(x);%函数2y3=exp(x);%函数3y4=sin(x).*cos(x);%函数4%%%%%%%%%%%%%%%%%%%%%%%%%在一幅图上绘制多幅小图%%%%%%%%%%%%%%%%%%%%%%%%%%%%figure(1)subplot(221),%图一plot(x,y1);%绘制y1gridon;%添加网格%axis([min(x)max(x)min(y1)max(y1)]);%指定显示范围subplot(222),%图二hist(y2);%绘制y2gridon;%添加网格%axis([min(x)max(x)min(y2)max(y2)]);%指定显示范围subplot(223),%图三stem(x,y3);%绘制y3gridon;%添加网格%axis([min(x)max(x)min(y3)max(y3)]);%指定显示范围subplot(224),%图四plot(x,y4,'rp');%绘制y4gridon;%添加网格%axis([min(x)max(x)min(y4)max(y4)]);%指定显示范围%%%%%%%%%%%%%%%%%%%%%%%%%%%%%画出一组二维图形%%%%%%%%%%%%%%%%%%%%%%%%%%%%%figure(2)a=linspace(0,2*pi,200);k=[1,2,3];y=sin(a')*k;plot(a,y(:,1),a,y(:,2),a,y(:,3));legend(['y=',num2str(k(1)),'*sin(x)'],['y=',num2str(k(2)),'*sin(x)']...,['y=',num2str(k(3)),'*sin(x)']);xlabel('x');ylabel('y');title('多条曲线绘制');gridon;%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%画出一组三维图形%%%%%%%%%%%%%%%%%%%%%%%%%%%%figure(3)kk=30;x=linspace(-5,5,kk);y=linspace(-5,5,kk);fori=1:kkforj=1:kkz(i,j)=sin(x(i))+cos(y(j));endendsurf(x,y,z);xlabel('x');ylabel('y');zlabel('z');title('z=sin^2(x)/(3*y-2)');%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%复数绘制%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%figure(4)clearkk=1:1:10;fori=1:10y(i)=sin(kk(i))+cos(kk(i))/kk(i)*j;endcompass(y);五、褶积的相关计算与编程（设计2）1.设计内容：计算普通褶积与循环褶积，分别使用时间域与频率域两种方法进行正、反演计算，指出循环褶积计算时所存在的边界效应现象；编写一个做相关分析的源程序。2.实验成果：（1）、构造如下两个向量：a=[1,2,3,4];b=[9,8,7,6];计算得到：线性褶积[9265080654624]循环次数时间域频率域循环褶积5[5550508065][5550508065]6[332650806546][332650806546]7[9265080654624][9265080654624]8[92650806546240][92650806546240]从计算结果可以看出，当循环次数小于N1+N2-1时，线性褶积和循环褶积不等，当循环次数大于等于N1+N2-1时，线性褶积和循环褶积相等。（2）、构造两个向量：a=[123];b=[1235];计算相关得到：频率域：[14131623]时间域（6次）：[148351323]程序：1、褶积%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%计算普通褶积与循环褶积，分别使用时间域与频率域两种方法%进行正、反演计算，指出循环褶积计算时所存在的边界效应现象；%编写一个做相关分析的源程序。%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%验证循环褶积和线性褶积在什么条件下相等%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%clc;clear;a=[1,2,3,4];%a矩阵b=[9,8,7,6];%b矩阵%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%kk1=length(a);kk2=length(b);%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%循环褶积时间域%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%xx=8;%循环次数手动更改aa=zeros(xx,1);aa(1:kk1,1)=a';%扩展abb=zeros(xx,1);bb(1:kk2,1)=b';%扩展bbb1=zeros(xx,xx);%循环矩阵fori=1:xxbb1(i:xx,i)=bb(1:xx-i+1);bb1(1:i-1,i)=bb(xx-i+2:xx);endok1=bb1*aa;%循环褶积结果%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%线性褶积时间域%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%bb2=zeros(kk1+kk2-1,kk1);fori=1:kk1bb2(i:i+kk2-1,i)=b(1:kk2)';endan=a';ok2=bb2*an;%线性褶积结果%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%循环褶积频率域%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%af=fft(aa);bf=fft(bb);ok3=ifft(af.*bf);2、相关%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%计算普通褶积与循环褶积，分别使用时间域与频率域两种方法进行%正、反演计算，指出循环褶积计算时所存在的边界效应现象；%编写一个做相关分析的源程序。%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%求两个一维数组的相关系数%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%clear;clc;a=[123];%数组a较短时可以手动输入b=[1235];%数组b较短时可以手动输入%a=csvread('**.csv',0,0);%数组a较长时可以读取csv文件%b=