信号与系统实验三.doc

信号与线性系统分析实验实验三：周期信号的傅利叶级数分析及MATLAB实现学院：信息学院 专业：通信工程(武警国防生) 指导教师：肖琦姓名：梁由勇 学号：20081060094 成绩： 实验目的：1.用MATLAB实现周期信号的傅利叶级数；2.用MATLAB实现周期信号(包括典型周期信号)的频谱分析；3.观察利用MATLAB生成的图形及结果，与信号与系统理论知识相连系，加深对信号与系统理论知识的深入理解。9.1 已知周期半波余弦信号和周期全波余弦信号的波形分别如图所示（图略），用MATLAB编程求出它们的傅里叶系数，绘出其直流、一次、二次、三次、四次及五次谐波叠加后的波形图，并将其与原周期信号的时域波形进行比较，观察周期信号的分解与合成过程。解：% 观察周期余弦半波信号的分解和合成% m:傅立叶级数展开的项数display(Please input the value of m (傅立叶级数展开的项数); m=input(m = ); t=-2.5*pi:0.01:2.5*pi; t1=-0.5*pi:0.01:0.5*pi;n=round(length(t)/5); f=cos(t1);zeros(n-1,1);cos(t1);zeros(n-1,1);cos(t1); y=zeros(m+1,max(size(t);y(m+1,:)=f;subplot(m+2),1,1)plot(t/pi,y(m+1,:); grid; axis(-2.5 2.5 -0.5 1.5); title(周期半波余弦信号); xlabel(t/pi,Fontsize, 8); x=zeros(size(t);kk=1; %计算系数syms tx n T=2*pi; fx=sym(cos(tx);Nn=30;an=zeros(m+1,1);bn=zeros(m+1,1);A0=2*int(fx,tx,-T/4,T/4)/T; An=2*int(fx*cos(2*pi*(n+eps/2)*tx/T),tx,-T/4,T/4)/T; Bn=2*int(fx*sin(2*pi*(n+eps/2)*tx/T),tx,-T/4,T/4)/T; an(1)=double(vpa(A0,Nn); an(2)=0.5;for k=2:m an(k+1)=double(vpa(subs(An,n,k),Nn); bn(k+1)=double(vpa(subs(Bn,n,k),Nn); end%计算直流分量pause;x=an(1)*cos(0*t)/2;plot(t/pi,y(m+1,:);hold on;plot(t/pi,x); grid;hold off;axis(-2.5 2.5 -0.5 1.5); title(直流分量);xlabel(t/pi,Fontsize, 8);%各次谐波叠加for k=1:m pause; x=x+an(k+1).*cos(k*t); y(k,:)=x;subplot(m+2),1,k+1); plot(t/pi,y(m+1,:); hold on; plot(t/pi,y(k,:); hold off; grid; axis(-2.5 2.5 -0.5 1.5); title(strcat(第,kk,次谐波叠加);xlabel(t/pi,Fontsize, 8);kk=strcat(kk,、,num2str(k+1);endpause;subplot(m+2),1,m+2)plot(t/pi,y(1:m+1,:);grid;axis(-2.5 2.5 -0.5 1.5); title(各次谐波叠加波形);xlabel(t/pi,Fontsize, 8);% End% 观察周期余弦全波信号的分解和合成% m:傅立叶级数展开的项数display(Please input the value of m (傅立叶级数展开的项数); t = -2.5*pi:0.01:2.5*pi; t1=-0.5*pi:0.01:0.5*pi-0.01;n = round(length(t)/5); f = cos(t1);cos(t1);cos(t1);cos(t1);cos(t1);0; y = zeros(m+1,max(size(t);y(m+1,:) = f; subplot(m+2,1,1)plot(t/pi,y(m+1,:); grid on; axis(-2.5 2.5 -0.2 1.2); title(周期全波余弦信号); xlabel(t/pi,Fontsize, 8); x=zeros(size(t);kk = 1; %计算系数syms tx n T=pi; fx=sym(cos(tx);Nn=32;an=zeros(m+1,1);bn=zeros(m+1,1);A0 =2*int(fx,tx,-T/2,T/2)/T; An=2*int(fx*cos(2*pi*(n+eps/2)*tx/T),tx,-T/2,T/2)/T; Bn=2*int(fx*sin(2*pi*(n+eps/2)*tx/T),tx,-T/2,T/2)/T; an(1) = double(vpa(A0,Nn); for k=1:m an(k+1)=double(vpa(subs(An,n,k),Nn); bn(k+1)=double(vpa(subs(Bn,n,k),Nn); end%求直流信号 pause;x=an(1)*cos(0*t)/2;subplot(m+2,1,1)plot(t/pi,y(m+1,:);hold on;plot(t/pi,x);grid on;hold off;axis(-2.5 2.5 -0.2 1.2);title(周期全波余弦信号);xlabel(t/pi,Fontsize, 8);%各次谐波叠加for k=1:mpause;x=x+an(k+1).*cos(2*k*t);y(k,:) = x; subplot(m+2,1,k+1)plot(t/pi,y(m+1,:);hold on; plot(t/pi,y(k,:);hold off;grid on;axis(-2.5 2.5 -0.2 1.2); title(strcat(第,kk,次谐波叠加);xlabel(t/pi,Fontsize, 8);kk = strcat(kk,、,num2str(k+1);endpause;subplot(m+2,1,m+2)plot(t/pi,y(1:m+1,:);grid on;axis(-2.5 2.5 -0.2 1.2);title(各次次谐波叠加波形);xlabel(t/pi,Fontsize, 8);% End9.2 试用MATLAB编程会出9.1中所示周期信号的幅度频谱，要求交互式输入信号周期，观察分析信号周期与频谱的关系。当周期T趋于无穷大时，频谱谱线将发生什么样的变化？解：syms T n t;display(Please input the value of NF,T,tao);Nf=input(Nf=);T=input(T=);tao=input(tao=);an=2/T*int(2/T*t*cos(2*pi*n*t/T),t,0,tao);bn=2/T*int(2/T*t*sin(2*pi*n*t/T),t,0,tao);a1n=zeros(1,Nf+1);b1n=zeros(1,Nf+1);cn=zeros(1,Nf+1);cn(1)=1/2;for i=2:Nf+1 a1n(i)=subs(an,n,i); b1n(i)=subs(bn,n,i); cn(i)=(a1n(i)2+b1n(i)2)(1/2);endk=0:Nf;stem(k,cn);hold onplot(k,cn);title(strcat(幅度频谱，周期、时域信号分别为,num2str(T),和,num2str(tao);xlabel(strcat(谐波次数,k); 运行：Please input the value of m (傅立叶级数展开的项数)Please input the value of m (傅立叶级数展开的项数)Please input the value of NF,T,taoNf=30T=2*pitao=pi/2tao=pitao=pi/4固定tao=1, Nf=30改变T分别为2*pi ,4*pi ,8*pi 图形分别如下：T=2*piT=8*piT=4*pi9.3 已知周期锯齿脉冲信号如图所示（图略），用MATLAB绘制其频谱，要求交互式设置信号周期和时域宽度，观察信号周期T及时域宽度对信号频谱的影响。解：在一个周期内而：首先求解其傅立叶系数：;编写.m文件如下：disp(please input the value of T ,tao and Nf);T=input(T=);tao=input(tao=);Nf=input(Nf=);syms x n kNn=32;An=zeros(Nf+1,1);Bn=zeros(Nf+1,1);f=x/tao;a0=2*int(f,x,0,tao)/T;an=2*int(f*cos(n*x),x,0,tao)/T;bn=2*int(f*sin(n*x),x,0,tao)/T;An(1)=