实验4连续信号与系统的频域分析及MATLAB实现

1、实验4连续信号与系统的频域分析及MATLAB实现1、 实验目的： 1.用MATLAB实现非周期连续信号的傅里叶变换，并绘制出幅度谱和相位谱，利用仿真结果进一步加深对理论知识的理解。 2.掌握连续信号傅里叶变换的数值近似计算方法，并验证傅里叶变换的各项性质。 3.掌握求解连续时间系统的频响函数H(jw)的方法,并绘图分析频响函数的特性。2、 实验内容10.1（3）：程序：syms t v w x phase im re;f=sin(2*pi*t)/(2*pi*t)2;Fw=fourier(f) subplot(311);ezplot(f)axis(-pi pi -1 2);title(原图);s

2、ubplot(312);ezplot(abs(Fw)axis(-6 6 -1 1);title(幅度谱);im=imag(Fw)re=real(Fw)phase=atan(im/re)subplot(313);ezplot(phase)axis(-6 6 -1 1);title(相位谱);w =1/8/pi*(-(-w+4*pi)*heaviside(w-4*pi)-(-w-4*pi)*heaviside(w+4*pi)-2*w*heaviside(w)im =-1/2*i*(1/8/pi*(-(-w+4*pi)*heaviside(w-4*pi)-(-w-4*pi)*heaviside(w+

3、4*pi)-2*w*heaviside(w)-1/8/pi*conj(-(-w+4*pi)*heaviside(w-4*pi)-(-w-4*pi)*heaviside(w+4*pi)-2*w*heaviside(w)re =1/16/pi*(-(-w+4*pi)*heaviside(w-4*pi)-(-w-4*pi)*heaviside(w+4*pi)-2*w*heaviside(w)+1/16/pi*conj(-(-w+4*pi)*heaviside(w-4*pi)-(-w-4*pi)*heaviside(w+4*pi)-2*w*heaviside(w) phase =-i*atanh(1/

4、2*(1/8/pi*(-(-w+4*pi)*heaviside(w-4*pi)-(-w-4*pi)*heaviside(w+4*pi)-2*w*heaviside(w)-1/8/pi*conj(-(-w+4*pi)*heaviside(w-4*pi)-(-w-4*pi)*heaviside(w+4*pi)-2*w*heaviside(w)/(1/16/pi*(-(-w+4*pi)*heaviside(w-4*pi)-(-w-4*pi)*heaviside(w+4*pi)-2*w*heaviside(w)+1/16/pi*conj(-(-w+4*pi)*heaviside(w-4*pi)-(-w

5、-4*pi)*heaviside(w+4*pi)-2*w*heaviside(w) 10.2（1）程序：syms t w ;F=8*(sin(w/4)2/(w)2;f=ifourier(F,t)ezplot(f);axis(-1 1 -0.3 1);title(时域波形)f =(2*t+1)*heaviside(t+1/2)+(2*t-1)*heaviside(t-1/2)-4*t*heaviside(t) 10.4程序：dt=0.005;t=-2:dt:2;f1=Heaviside(t+1)-Heaviside(t-1);subplot(2,2,1)plot(t,f1)axis(-2 2 0

6、 1.5);title(f1(t);f=dt*conv(f1,f1)n=-4:dt:4;subplot(2,2,2)plot(n,f)title(f(t)=f1(t)*f1(t);axis(-4 4 0 2.5);W1=2*pi*5;N=200;k=-N:N;W=k*W1/N;F1=f1*exp(-j*t*W)*dt;F1=abs(F1)F=f*exp(-j*n*W)*dt;F=abs(F)F=F.*Fsubplot(2,2,3)plot(W,F1)subplot(2,2,4)plot(W,F)axis(-10*pi 10*pi 0 10);axis(-10*pi 10*pi 0 20);10.5 程序：b=0 0 2;a=0.04 0.4 2;h,w=freqs(b,a,100);h1=abs(h);h2=angle(h);subplot(2,1,1)plot(w,h1)hold onaxis(0 60 0 1.6);gridxlabel(角频率);ylabel(幅度);title(幅频特性);subplot(2,1,2)plot(w,h2*180/pi)axis(0 150 -250 0);gridxlabel(角频率);ylabel(幅度);title(相频特性);实验小结： 通过实验我对理论知识有了更深刻的理解，当周期信号的周期无限增大时，周期信号就转换