function Ly_sita = diff_LY(Xs_fft,id_v,delta)
 
d_a=0.04;
vs=345;
L=6;
fs=48e3;
num1=1024;
f_s=fs/num1;
id_l=length(id_v);

      
          Yw=[];
          Aw=[]; 
   syms sita;       
   for lp2 = 1:id_l
       
         Xw=Xs_fft(id_v(lp2),:).';
         Yw=[Yw;Xw];
         
         fk=id_v(lp2)*f_s;
         af=exp(-j*2*pi*fk*d_a*[0:L-1].'*sin(sita*pi/180)./vs);
         Bf=[];
         if lp2==1
             Bf = [af;zeros((id_l-1)*L,1)];
         else 
             Bf_l=zeros((lp2-1)*L,1);
             Bf_r=zeros((id_l-lp2)*L,1);
             Bf = [Bf_l;af;Bf_r];
         end
         
%          Af((lp2-1)*L+1:(lp2-1)*L+L,:) = af;
         
         Aw=[Aw Bf];
      
     end
     
     mtx=(1/L).*eye(id_l);
     knerl=eye(id_l*L)-(Aw*mtx*Aw');
     Ly=(1/delta^2).*Yw'*knerl*Yw;
     Ly_sita=diff(Ly,sita,1);