信号与系统实验第九章

1、9.1已知周期半波余弦信号的波形如图9-15（a）所示，用MATLAB编程求出其傅里叶系数，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：（a）的表达式f(t)=0.5*(cos(t)+|cos(t)|)，周期为2*pi；display('Please input the value of m (傅里叶级数展开的项数)'); m = input('m = '); t = -3*pi:0.01:3*pi; n = round(length(t)/4); f=cos(t).*(

2、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('半波余弦信号'); xlabel('单位pi','Fontsize', 8); x = zeros

3、(size(t);kk = '1'y(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/(k2-1)*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

4、9;,'Fontsize', 8); kk = strcat(kk,'、',num2str(k);endpause;plot(t/pi,y(1:m+1,:);grid;axis(-3 3 -1 1.5);title('谐波叠加');xlabel('单位pi','Fontsize', 8);运行程序：Please input the value of m (傅里叶级数展开的项数)m = 89、3display('Please input the value of T,tao and Nf');T=in

5、put('T=');tao=input('tao=');Nf=input('Nf=');syms t n k xNn=32;an=zeros(Nf+1,1);bn=zeros(Nf+1,1);phase=zeros(Nf+1,1);f=x/tao;A0=2*int(f,x,0,tao)/T;As=2*int(f*cos(n*x),x,0,tao)/T;Bs=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(As,n,k),N

6、n); bn(k+1)=double(vpa(subs(Bs,n,k),Nn);endcn=sqrt(an.*an+bn.*bn);t=-T*5:0.1:T*5;d=-T*5:T:T*5;xx=pulstran(t,d,'tripuls',tao,1);subplot(211);plot(t+tao/2,xx)axis(-T*5 T*5 0 1.1);s1=strcat('周期锯齿脉冲信号',num2str(T), ' Tao= ',num2str(tao),'t');xlabel(s1,'Fontsize',8);subplot(212);k=0:Nf;stem(k,cn)hold onplot