function [xi_til, sigma_til ] = RangeRadar_split_augX_to_sigma_xi(X_til, ...
                                f_LC, tau, k, B, T, q, sgm)

n = length(X_til)/2;

if(length(tau) - n)
    sprintf('Size Wrong')
    return
end

if (1)
    [temp, S_til] = sort(abs(X_til(1:n)),'descend');
    %S_til = S_til(1:ceil(n*0.1)); % pick first 10% large elemenets % <=== no need
    temp = -( X_til(n+1:2*n)./X_til(1:n) )/(2i*pi*B  *sgm);
    xi_til = zeros(n,1); xi_til(S_til) = real(temp(S_til));
    sigma_til =   X_til(1:n) ./ ...
                         ( f_LC(-tau) .* f_LC(-xi_til) .* exp(2i*pi*q*(k'.*xi_til)/T) ) ; 
else
    sigma_til =  X_til./ f_LC(-tau) ;                  
end

%%