[z]=LSProny_T2star_regul_changed(T,t0,N,M,lambda, betta)

% Description: perform HR with regularization on |z|
%              lambda, betta - regularization parameters (in the paper: alpha and lambda)
%              lambda=|z|, betta=weighting between data and regularization terms
%
% % Hien Minh Nguyen, ECE, University of Illinois at Urbana-Champaign, Dec 14, 2007
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

function [z]=LSProny_T2star_regul_changed(T,t0,N,M,lambda, betta)  

c=t0(1:(M+1-N),1).'; 
r=t0((M+1-N):M,1).';
A=hankel(c,r);
y=[t0(N+1:M+1,1)];  
Ay=[A y];

By=conj(fliplr(Ay));

k=[N:-1:1].';
lvec=[lambda.^k; 1];
cvec=flipud(conj(lvec))./lvec;

for k=1:size(By,1)
    By(k,:)=By(k,:).*conj(cvec.');
end;

B=By(:,1:(size(By,2)-1)).*betta;
y1=By(:,end).*betta;

Y=[A;B];
y=-[y;y1];  

p=pinv(Y)*y;
         
sp=eye(N-1,N-1);    
C=[zeros(1,N-1);sp];
C=[C -p];
z=eig(C);   

% Sorting z by angle(z)
[phi,order]=sort(angle(z));                      
z=z(order);