MATLAB傅里叶变换及性质

1、使用MATLAB命令求出下列信号的傅里叶变换，并绘出其幅度谱和相位谱。(1)clear all;delta=0.03;t=-10:delta:10;w=-10:delta:10;ft1=sin(2*pi*(t-1))./(pi*(t-1));Fw=delta*ft1*exp(-j*t'*w);abs=abs(Fw);ang=angle(Fw);subplot(211);plot(w,abs),axis([-10,10,-0.5,1.5]),title('f1(t)频谱图'),grid onsubplot(212);plot(w,ang),axis([-10,10,-4,4]),title('f1(t)相位图'),grid on(2)clear all;delta=0.03;t=-10:delta:10;w=-10:delta:10;ft2=sinc(pi*t).^2;Fw=delta*ft2*exp(-j*t'*w);abs=abs(Fw);ang=angle(Fw);subplot(211);plot(w,abs),axis([-10,10,-0.5,1]),title('f2(t)频谱图'),grid onsubplot(212);plot(w,ang),axis([-10,10,-0.000015,0.000015]),title('f2(t)相位图'),grid on2、使用MATLAB命令求下列信号的傅里叶反变换，并绘出其时域信号图。(1)clear alldelta=0.01;t=-10:delta:10;w=-10:delta:10;Fw1=(10./(3+j*w))+(4./(5+j*w));ft1=delta./(2*pi)*(Fw1*exp(-j*w'*t));plot(t,ft1);title('f1(t)时域信号'),grid on(2)clear alldelta=0.01;t=-10:delta:10;w=-10:delta:10;Fw2=(2*w)./(j*(16+w.*w));ft2=delta*(Fw2*exp(-j*w'*t))./(2*pi);plot(t,ft2);title('f2(t)时域信号'),grid on3、利用MATLAB数值法分别绘出下列所示信号的幅度谱(1) clear all;delta=0.003;t=-2:delta:2;w=-40:delta:40;ft1=stepfun(t,-1)-stepfun(t,1);Fw1=delta*ft1*exp(-j*t'*w);abs=abs(Fw1);subplot(311);plot(t,ft1);axis([-2,2,-0.5,1.5]);title('时域信号'),grid onsubplot(312);plot(w,Fw1),axis([-40,40,-0.5,2]);title('频域'),grid onsubplot(313)plot(w,abs);axis([-40,40,0,2]);title('幅度谱'),grid on(2)clear all;delta=0.003;t=-2:delta:2;w=-20:delta:20;ft2=tripuls(t,2);Fw2=delta*ft2*exp(-j*t'*w);abs=abs(Fw2);subplot(311);plot(t,ft2);axis([-2,2,-0.5,1.5]);title('时域信号'),grid onsubplot(312);plot(w,Fw2),axis([-10,10,-0.5,1.5]);title('频域'),grid onsubplot(313)plot(w,abs);axis([-10,10,0,1.5]);title('幅度谱'),grid on4、设矩形信号，利用Matlab命令绘出该信号及其频谱图。同时绘出的频谱图，并加以比较。clear alldetla=0.007;t=-10:detla:10;w=-20:detla:20;a=0.5;t1=a*tft1=heaviside((t1+0.5))-heaviside((t1-0.5));Fw1=detla*ft1*exp(-j*((t)')*w);abs1=abs(Fw1);ang1=angle(Fw1);b=2;t2=b*tft2=heaviside((t2+0.5))-heaviside((t2-0.5));Fw2=detla*ft2*exp(-j*((t)')*w);abs2=abs(Fw2);ang2=angle(Fw2);subplot(421);plot(t,ft1),title('f(t/2)时域图'),grid onsubplot(423);plo