实验三周期信号的傅里叶级数分析及MATLAB实现.docxVIP

实验三周期信号的傅里叶级数分析及MATLAB实现一、实验目的：利用MATLAB实现周期信号的分解与合成，并图示仿真结果；用MATLAB实现周期信号的频谱，画图观察和分析周期信号的频谱；通过MATLAB对周期信号频谱的仿真，进一步加深对周期信号频谱理论知识的理解。实验内容9.1（a）：程序：display(Please input the value of m(傅里叶级数展开项数));m=input(m=);t=-3*pi:0.01:3*pi;n=round(length(t)/4);f=cos(t).*(heaviside(t+2.5*pi)-heaviside(t+1.5*pi)+heaviside(t+0.5*pi)-heaviside(t-0.5*pi)+heaviside(t-1.5*pi)-heaviside(t-2.5*pi));y=zeros(m+1,max(size(t)));y(m+1,:)=f;figure(1);plot(t/pi,y(m+1,:));grid;axis([-3 3 -1 1.5]);title(半波余弦);xlabel(单位:pi,Fontsize,8);x=zeros(size(t));kk=1;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)/Tan=2*int(fx*cos(2*pi*(n+eps/2)*tx/T),tx,-T/4,T/4)/Tbn=2*int(fx*sin(2*pi*(n+eps/2)*tx/T),tx,-T/4,T/4)/TAn(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));endy(1,:)=1/pi;y(2,:)=1/pi+1/2*cos(t);x=1/pi+1/2*cos(t);for k=2:6 pause; x=x+(-2*cos(pi*k/2)/pi/(k^2-1))*cos(k*t); y((k+1),:)=x; plot(t/pi,y(m+1,:)); hold on; plot(t/pi,y((k+1),:)); hold off; grid; axis([-3 3 -1 1.5]); title(strcat(第,kk,次谐波叠加)); xlabel(单位:pi,Fontsize,8); kk=strcat(kk,`,num2str(k));endpause;plot(t/pi,y(m+1,:));grid;axis([-3 3 -1 1.5]);title(谐波叠加);xlabel(单位:pi,Fontsize,8);a0 =2/pian =162259276829213363391578010288128*(-sin(9007199254740991/18014398509481984*pi)*cos(1/2*pi*n)+cos(9007199254740991/18014398509481984*pi)*sin(1/2*pi*n))/(-81129638414606681695789005144063+18014398509481984*n+81129638414606681695789005144064*n^2)/pibn =09.3：display(Please input the value of T,tao and Nf);T=input(T=);tao=input(tao=);Nf=input(Nf=);syms xnkNn=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)=double(vpa(a0,Nn));for k=1:Nf An(k+1)=double(vpa(subs(an,n,k),Nn)); Bn(k+1)=double(vpa(subs(bn,n,k),Nn));endcn=sqrt(An.*An+Bn.*Bn);m=0:Nf;stem(m,cn);hold on;plot(m,cn);xlabel(幅度谱\omega,Fontsize,8)Please input the