close all,clear all,clc;
fs=5.0e11;       
 
tr=0.11e-9;
tc=0.5e-9;
E=1; 

t=0:1/fs:1e-9-1/fs;       
w=sqrt(8*E/3/tr)*(1-4*pi*(((t-tc)/tr).^2)).*exp(-2*pi*(((t-tc)/tr).^2));
figure,hold on,grid on;
plot(t,w/max(w));
xlabel('t/s','color','r');
ylabel('w(t)','color','r');

N=length(w);
W=fft(w);
W=10^(-4.13)*abs(W)./max(abs(W)); 
W=log10(W)*10;                    
 
f=[-N/2:1:N/2-1]*fs/N;
figure,hold on,grid on;
plot(f/1.0e9,fftshift(W));               
set(gca,'xlim',[0 12],'ylim',[-80 -40]);