周期信号的傅里叶级数分析

第9章周期信号的傅里叶级数分析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，用MATLAB编程求出它实验代码如下：%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('Pleaseinputthevalueofm(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)';eros(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([-2.52.5-0.51.5]);title(' 期 半 波 余xlabel('t/pi','Fontsize',8);x=zeros(size(t));kk='1';%计算系数symstxnT=2*pi;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;fork=2:man(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,:));holdon;

弦 信 号 ');plot(t/pi,x);grid;holdoff;axis([-2.52.5-0.51.5]);title('直流分量');xlabel('t/pi','Fontsize',8);%fork=1:mpause;x=x+an(k+1).*cos(k*t);y(k,:)=x;subplot((m+2),1,k+1);plot(t/pi,y(m+1,:));holdon;plot(t/pi,y(k,:));holdoff;grid;axis([-2.52.5-0.51.5]);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([-2.52.5-0.51.5]);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('Pleaseinputthevalueofm(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,:));gridon;axis([-2.52.5-0.21.2]);title(' 周 期 全 波 余 弦 信 号 ');xlabel('t/pi','Fontsize',8);x=zeros(size(t));kk='1';%计算系数symstxnT=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));fork=1:man(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;subplot(m+2,1,1)plot(t/pi,y(m+1,:));holdon;plot(t/pi,x);gridon;holdoff;axis([-2.52.5-0.21.2]);title('周期全波余弦信号');xlabel('t/pi','Fontsize',8);%各次谐波叠加fork=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,:));holdon;plot(t/pi,y(k,:));holdoff;gridon;axis([-2.52.5-0.21.2]);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,:));gridon;axis([-2.52.5-0.21.2]);title('各次次谐波叠加波形');xlabel('t/pi','Fontsize',8);%End实验截图如下：试用MATLAB9.1中所示周期信号的幅度频谱，要求交互输入信号周期观察分析周期信号与频谱的关系。当周期T趋于无穷大时，频谱谱线将发生什么样的变化？实验代码如下：symsTnt;display('PleaseinputthevalueofNF,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;fori=2:Nf+1a1n(i)=subs(an,n,i);b1n(i)=subs(bn,n,i);cn(i)=(a