clg
t1=[0:63]*2*pi/7;
% t1 gives a frequency that is not one of the FFT freqs
t2=[0:63]*2*pi/8;
a1=1;
a2=.5;
x=a1*exp(i*t1) + a2*exp(i*t2);
subplot(211);
plot([0:63],real(x));
v=axis;
axis([0 64 v(3) v(4)]);
title('Re(X) Time Series');
ylabel('Amplitude');
xlabel('index k');

axis;
subplot(212);
y=fft(x);
plot([1:64],2*log10(abs(y)));
v=axis;
axis([0 64 v(3) v(4)]);
xlabel('Frequency index j');
ylabel('LOG_10(ABS(Y^2))');
axis;
title('Periodogram of X with N=64');
%gtext('X = a1*exp(i*[1:64]*2*pi/7) + a2*exp(i*[1:64]*2*pi/8)');
print -deps pgram2