% Fourier transform of a wave packet



n=11;

N=2^n;

L=20;

dx=2*L/N;

x=-L:dx:L-dx;



b=5;

a=0.05;



envelope=b*exp(-a*x.^2);

y=envelope.*cos(b*x);

Y=fft(y);

M=max(max(abs(real(Y))));



figure(1)

subplot(3,1,1)

plot(x,y,x,envelope,'r--',x,-envelope,'r--')

xlabel('x')

ylabel('y(x)')

axis([-L L -b-2 b+2]);

title('Wave packet y(x) with enevelope and its Fourier transform Y(w)')

subplot(3,1,2)

plot(abs(real(Y(1:N/2))))

xlabel('w')

ylabel('Y(w)')

axis([0 N/2 -M/10 M+M/10])

subplot(3,1,3)

plot(abs(real(Y(1:N/2))),'.-','MarkerSize',14)

xlabel('w')

ylabel('Y(w)')

axis([0 100 -M/10 M+M/10])