% MATLAB script for Illustrative Problem 9, Chapter 7.
clear
echo on
K=10;N=2*K;T=100;
a=rand(1,36);
a=sign(a-0.5);
b=reshape(a,9,4);
% Generate the 16QAM points
XXX=2*b(:,1)+b(:,2)+j*(2*b(:,3)+b(:,4));
XX=XXX';
X=[0 XX 0 conj(XX(9:-1:1))];
xt=zeros(1,101);
for t=0:100
  for k=0:N-1
    xt(1,t+1)=xt(1,t+1)+1/sqrt(N)*X(k+1)*exp(j*2*pi*k*t/T);
    echo off
  end
end
echo on
xn=zeros(1,N);
for n=0:N-1
  for k=0:N-1
    xn(n+1)=xn(n+1)+1/sqrt(N)*X(k+1)*exp(j*2*pi*n*k/N);
    echo off
  end
end
echo on
pause % press any key to see a plot of x(t)
plot([0:100],abs(xt))
% Check the difference between xn and samples of x(t)
for n=0:N-1
  d(n+1)=xt(T/N*n+1)-xn(1+n);
  echo off
end
echo on
e=norm(d);
Y=zeros(1,10);
for k=1:9
  for n=0:N-1
    Y(1,k+1)=Y(1,k+1)+1/sqrt(N)*xn(n+1)*exp(-j*2*pi*k*n/N);
    echo off
  end
end
echo on
dd=Y(1:10)-X(1:10);
ee=norm(dd);