function [Shat,Omega] = SPECTREgen(S,T); 
N    = length(S)-1; S(1) = (S(1)+S(N+1))/2;  
u    = fft(S(1:N)');
k = 1:N; w = ((-1).^(k-1))'; 
u    = w.*u; u1 = u(1:fix(N/2))'; u2 = u(fix(N/2)+1:N)'; 
Shat = (2*T/N)*[u2 u1 0]; Omega = N/(4*T);  
end

