function [ddlss dlss A_plus AA_inv A_der_plus] = ddm_der_lin_sys_sol(A_sys,b_sys,A_der_sys,b_der_sys,N_fft,R,Q)
dlss = zeros(Q+1, N_fft-R+1);
ddlss = zeros(Q+1, N_fft-R+1);

for l=1:N_fft-R+1
  A = A_sys(:,:,l);
  b = b_sys(:,:,l);

  
  AA_inv = inv(A'*A);
  A_plus = AA_inv*A';
  ddm_est_  = fliplr((A_plus * b).');
  dlss(:,l) = [ddm_est_ 0];
  
  A_der = A_der_sys(:,:,l);
  b_der = b_der_sys(:,:,l);  
  AA_mix = ( A_der' * A + A' * A_der );
  A_der_plus = (-AA_inv * AA_mix * AA_inv * A' + AA_inv * A_der');
  ddm_est_der_ = fliplr((A_der_plus *b + A_plus * b_der).');
  ddlss(:,l) = [ddm_est_der_ 0];
  
end
end