7.1傅里叶变换的实现7.1.1MATLAB符号运算求解法>>ft=sym('exp(-2*t)*Heaviside(t)');>>Fw=fourier(ft)Fw=1/(2+i*w)>>symst>>FW=sym('1/(1+w^2)');>>ft=ifourier(Fw,t)ft=exp(-2*t)*heaviside(t)>>ft=sym('exp(-2*t)*Heaviside(t)');>>FW=fourier(ft);>>subplot(211)>>ezplot(abs(FW));gridon>>title('幅度值')>>phase=atan(imag(FW)/real(FW));>>subplot(212)>>ezplot(phase);gridon>>title('相位图')>>ft=sym('4*cos(2*pi*6*t)*(Heaviside(t+1/4)-Heaviside(t-1/4))');>>FW=simplify(fourier(ft))FW=8*w*sin(1/4*w)/(-w^2+144*pi^2)>>subplot(121)>>ezplot(ft,[-0.50.5]),gridon>>subplot(122)>>ezplot(abs(FW),[-24*pi24*pi]),gridon7.2傅里叶变换的性质7.1.2尺度变换的性质>>ft1=sym('Heaviside(t+1/2)-Heaviside(t-1/2)');>>subplot(321)>>ezplot(ft1,[-1.51.5]),gridon>>FW1=simplify(fourier(ft1));>>subplot(322)>>ezplot(abs(FW1),[-10*pi10*pi]),gridon>>axis([-10*pi10*pi-0.22.2])>>ft2=sym('Heaviside(t/2+1/2)-Heaviside(t/2-1/2)');>>subplot(323)>>ezplot(ft2,[-1.51.5]),gridon>>FW2=simplify(fourier(ft2));>>subplot(324)>>ezplot(abs(FW2),[-10*pi10*pi]),gridon>>axis([-10*pi10*pi-0.22.2])>>ft3=sym('Heaviside(2*t+1/2)-Heaviside(2*t-1/2)');>>subplot(325)>>ezplot(ft3,[-1.51.5]),gridon>>FW3=simplify(fourier(ft3));>>subplot(326)>>ezplot(abs(FW3),[-10*pi10*pi]),gridon>>axis([-10*pi10*pi-0.22.2])第八章拉普拉斯变换>>F=sym('s^2/(s^2+1)');>>ft=ilaplace(F)ft=dirac(t)-sin(t)>>formatrat;>>B=[1,2];>>A=[1,4,3,0];>>[r,p]=residue(B,A)%F(s)的部分分式展开式r=-1/6-1/22/3p=-3-10拉普拉斯变换法求解微分方程symstsYzis=(3*s+13)/(s^2+3*s+2);yzi=ilaplace(Yzis)xt=4*exp(-2*t)*Heaviside(t);Xs=laplace(xt);Yzss=Xs/(s^2+3*s+2);yzs=ilaplace(Yzss)yt=simplify(yzi+yzs)第九章连续时间LTI系统的频率特性连续时间LTI系统的频域分析t=0:0.1:20;w1=1;w2=10;H1=1/(-w1^2+j*3*w1+2);H2=1/(-w2^2+j*3*w2+2);f=5*cos(t)+2*cos(10*t);y=abs(H1)*cos(w1*t+angle(H1))+abs(H2)*cos(w2*t+angle(H2));subplot(2,1,1)plot(t,f);gridonylabel('f(t)'),xlabel('Time(s)')title('输入信号的波形')subplot(2,1,2)plot(t,y);gridonylabel('y(t)'),xlabel('Time(s)')title('稳态响应的波形')