习题一绘制典型信及其频谱图

1、习题一绘制典型信号及其频谱图四个常用信号及其傅里叶变换式如表1所示。表1常用信号的傅里叶变换表信号名称时间函数f(t)频谱函数F(®)单边指数脉冲Ee-atu(t)(a>0)Ea+jw矩形脉冲VrE01Tt<2丿丿EtSa(Tk2丿2E.=sinwWT)k2丿升余弦脉冲vrE2_(2nt1+cos1IT丿04<2EtSaWT、k2丿0(tkT)_"2丿21"I<2n丿)三角脉冲f(2ItlE111IT0IT、q<-1LTt>-2/丿Et(wt、Sa22k4y8E.=si丿w2TWT)nk4丿绘制单边指数信号及其频谱图的MATLA

2、B程序如下：closeall;E=1;a=1;t=0:0.01:4;w=-30:0.01:30;f=E*exp(-a*t);F=1./(a+j*w);plot(t,f);xlabel('t');ylabel('f(t)');figure;plot(w,abs(F);xlabel('omega');ylabel('|F(omega)|');figure;plot(w,20*log10(abs(F);xlabel('omega');ylabel('|F(omega)|indB');figure;plot

3、(w,angle(F);xlabel('omega');ylabel('phi(omega)');请更改参数，调试此程序，绘制单边指数信号的波形图和频谱图。观察参数a对信号波形及其频谱的影响。(2)绘制矩形脉冲信号、升余弦脉冲信号和三角脉冲信号的波形图和频谱图，观察并对比各信号的频带宽度和旁瓣的大小。习题一绘制典型信号及其频谱图©(1)a=1时:00.511.52.533.542t-30-20-101020300©-30-20-100102030-30-20-101020300©a=10时：00.511.522.533.54t30-

4、33比较图像可知：a越小，波形下降越慢，高频成分越少，低频成分越多，频谱越集中，频谱的相位越大。a越大，波形下降越快，高频成分越多，低频成分越少，频谱越分散，频谱的相位越小。2)矩形脉冲信号：-2-1.5-1-0.500.511.52t-30-20-100102030©升余弦脉冲信号：-2-1.5-1-0.500.511.52t三角脉冲信号：LLL1111|1J1i11f1l'1:.!l"rr1110.90.80.70.60.50.40.30.20.10-2-1.5-1-0.500.511.52t比较图像可知：矩形脉冲信号的带宽为2n,升余弦脉冲信号和三角脉冲信号的

5、带宽为4n。旁瓣由小到大依次是升余弦脉冲信号、三角脉冲信号、矩形脉冲信号。代码：矩形脉冲信号：closeall;E=1;tao=1;t=-2*tao:0.01:2*tao;w=-30:0.01:30;f=E*(heaviside(t+tao/2)-heaviside(t-tao/2);F=(2.*E./w).*sin(w.*tao./2);plot(t,f);xlabel('t');ylabel('f(t)');figure;plot(w,F);xlabel('omega');ylabel('F(omega)');升余弦脉冲信号：

6、closeall;E=1;tao=1;t=-2*tao:0.01:2*tao;w=-30:0.01:30;f=E/2*(1+cos(2*pi*t/tao).*(heaviside(t+tao/2)-heaviside(t-tao/2);F=(E*sin(w*tao/2)./(w.*(1-(w*tao/2/pi).2);plot(t,f);xlabel('t');ylabel('f(t)');figure;plot(w,abs(F);xlabel('omega');ylabel('F(omega)');三角脉冲信号：closeall;E=1;tao=1;t=-2*tao:0.01:2*tao;w=-30:0.01:30;f=E*(1-2*abs(t)/tao).*(heaviside(t+tao/2)-heaviside(t-tao/2);F=(8*E*sin(w*tao/4).A2)./(w.A2*tao);plot(t,f);xlabel(&