信号与系统实验第九章

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).*(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(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/(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));

end

pause;

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 = 8

9、3

display('Please input the value of T,tao and Nf'); T=input('T=');

tao=input('tao=');

Nf=input('Nf=');

syms t n k x

Nn=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),Nn));

bn(k+1)=double(vpa(subs(Bs,n,k),Nn));

end

cn=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 on

plot(k,cn);

xlabel('幅度谱\omega','Fontsize',8);

Please input the value of T,tao and Nf

T=