ex_2.m

信号与系统分析以matlab实现

%P188 3
%三角波
clear all;syms t x n t0;
T=4;Nf=60;Nn=6;
x=sym('(1-abs(t))')
A0=int(x,t,-2,2)/T
As=int(symmul(x,2*cos(2*pi*n*t/T)/T),t,-2,2)
Bs=int(symmul(x,2*sin(2*pi*n*t/T)/T),t,-2,2)
Fn=symsub(As,j*Bs)/2
A(1)=double(vpa(A0,Nn));
for k=1:Nf
     A(k+1)=double(vpa(subs(As,n,k),Nn));
     B(k+1)=double(vpa(subs(Bs,n,k),Nn));
end
A
t1=-2:0.01:2;
y=subs(x,t,t1);
figure(1)
subplot(3,1,1),plot(t1,y),title('矩形脉冲')
%单边谱
Fs(1)=A(1);
Fs(2:Nf+1)=abs(A(2:Nf+1)-j.*B(2:Nf+1))/2;
Ns=0:Nf;
subplot(3,1,2),stem(Ns,Fs),title('连续时间函数的单边谱')
%双边谱
N=Nf*2*pi/T;
K=-N:2*pi/T:N;
Fd=[fliplr(Fs),Fs(2:Nf+1)];
subplot(3,1,3),stem(K,Fd),title('连续时间函数的双边谱')
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%5
%方波
clear all;syms t x n t0;
T=4;Nf=60;Nn=6;
x=sym('-Heaviside(t+2)+2*Heaviside(t+1)-2*Heaviside(t-1)+Heaviside(t-2)')
A0=int(x,t,-2,2)/T
As=int(symmul(x,2*cos(2*pi*n*t/T)/T),t,-2,2)
Bs=int(symmul(x,2*sin(2*pi*n*t/T)/T),t,-2,2)
Fn=symsub(As,j*Bs)/2
A(1)=double(vpa(A0,Nn));
for k=1:Nf
     A(k+1)=double(vpa(subs(As,n,k),Nn));
     B(k+1)=double(vpa(subs(Bs,n,k),Nn));
end
t1=-2:0.01:2;
y=subs(x,t,t1);
figure(2)
subplot(3,1,1),plot(t1,y),title('矩形脉冲')
%单边谱
Fs(1)=A(1);
Fs(2:Nf+1)=abs(A(2:Nf+1)-j.*B(2:Nf+1))/2;
Ns=0:Nf;
subplot(3,1,2),stem(Ns,Fs),title('连续时间函数的单边谱')
%双边谱
N=Nf*2*pi/T;
K=-N:2*pi/T:N;
Fd=[fliplr(Fs),Fs(2:Nf+1)];
subplot(3,1,3),stem(K,Fd),title('连续时间函数的双边谱')