clear all
tau=10e-11;fc=7e9;
N=3;
NN=N+1;
for nn=1:NN;
    n=nn-1;
    E(nn)=1;
    k(nn)=sqrt(E(nn)/tau/factorial(n)/sqrt(2*pi));
end;
it=0;
for t=-1e-9:5e-12:1e-9;
    it=it+1;
    for nn=1:NN;
        n=nn-1;
        hh=0;
        for i=0:fix(n/2);
            hh=hh+(-.5)^i*(t/tau)^(n-2*i)/factorial(n-2*i)/factorial(i);
        end;
        h(nn,it)=k(nn)*exp(-t^2/4/tau^2)*factorial(n)*hh;
        p(nn,it)=sqrt(2)*h(nn,it)*cos(2*pi*fc*t);
    end,
end;
figure (1);t=-1e-9:5e-12:1e-9;
for nn=1:NN;
    if nn==1;co='r';end;if nn==2;co='g';end;if nn==3;co='b';end;if nn==4;co='c';end;if nn==5;co='k';end;if nn==6;co='m';end;if nn==7;co='y';end;
    plot(t,p(nn,:),co);hold on;
end;
legend('n=0','n=1','n=2','n=3');
xlabel('Time, sec');ylabel('Amplitude');grid;
  
iif=0;
for f=0:2e6:1.2e10;
    iif=iif+1;
    P_0(iif)=(sqrt(2)/2)*k(1)*tau*2*sqrt(pi)*exp(-(2*pi*tau*(f-fc))^2);
    P_1(iif)=(sqrt(2)/2)*k(2)*tau*(-j*4*pi*(f-fc)*tau)*2*sqrt(pi)*exp(-(2*pi*tau*(f-fc))^2);
    P_2(iif)=(sqrt(2)/2)*k(3)*tau*(1-16*pi^2*(f-fc)^2*tau^2)*2*sqrt(pi)*exp(-(2*pi*tau*(f-fc))^2);
    P_3(iif)=(sqrt(2)/2)*k(4)*tau*(-j*12*pi*(f-fc)*tau+j*64*pi^3*(f-fc)^3*tau^3)*2*sqrt(pi)*exp(-(2*pi*tau*(f-fc))^2);
end,
figure (3);f=0:2e6:1.2e10;plot(f,abs(P_0),'r');hold on;plot(f,abs(P_1),'g');hold on;plot(f,abs(P_2),'b');hold on;plot(f,abs(P_3),'c');
legend('n=0','n=1','n=2','n=3');
xlabel('Frequency, Hz');ylabel('Magnitude');grid;