a=0;
nav=10;
n=256;

t1=[1:nav*256]*2*pi/8;
a1=1;
x=a1*exp(i*t1);
sig=2;
x=x+sig*randn(size(x))+i*sig*randn(size(x));
subplot(211);
plot(real(x(1:256)));
v=axis;
axis([v(1) 256 v(3) v(4)]);
title('Re(X) Time Series');




% now do nav scans, average and plot
yav=zeros(1,256);
start=1;
stop=256;
for j=1:nav
	y=fft(x(start:stop));	
	yav = yav + abs(y).*abs(y);
	start=start+256;
	stop=stop+256;
end
subplot(212);
plot(log10(yav/nav));
v=axis;
axis([v(1) n 2 7]);
title(['Average of ',int2str(nav),' Log Periodograms with N=256 and sigma_Y = ',num2str(sqrt(2*sig))]);
xlabel('Frequency Index j');
ylabel('LOG10');

nper=256/8;
yav=[yav(1:nper),yav(nper+2:length(yav))];
avnoise=log10(mean(yav/nav))
gtext(['LOG10 average of noise-only squares: ',num2str(avnoise)]);

print -deps  pgram6