func_lev_durb (y, M);

%function of levinsonDurbin__Hamza

function [aCoeff, tcount_of_aCoeff, e] = func_lev_durb (y, M);

%M=how much, how much order?
if (nargin<2), M = 10; end   %prediction order=10; 

sk=0;       %initializing summartion term "sk"
a=[zeros(M+1);zeros(M+1)]; %defining a matrix of zeros for "a" for init.

%MAIN BODY OF THIS PROGRAM STARTS FROM HERE>>>>>>>>>>>>>>
z=xcorr(y);

%finding array of R[l]
R=z( ( (length(z)+1) ./2 ) : length(z)); %R=array of "R[l]", where l=0,1,2,
                                         %...(b+N)-1
                                         %R(1)=R[lag=0], R(2)=R[lag=1], 
                                         %R(3)=R[lag=2]... etc 

%GETTING OTHER PARAMETERS OF PREDICTOR OF ORDER "0":
s=1;        %s=step no.
J(1)=R(1);          %J=array of "Jl", where l=0,1,2...(b+N)-1
                    %J(1)=J0, J(2)=J1, J(3)=J2 etc

%GETTING OTHER PARAMETERS OF PREDICTOR OF ORDER "(s-1)":
for s=2:M+1,
    sk=0;               %clearing "sk" for each iteration
    for i=2:(s-1),
        sk=sk + a(i,(s-1)).*R(s-i+1);
    end                 %now we know value of "sk", the summation term
                        %of formula of calculating "k(l)"
    k(s)=(R(s) + sk)./J(s-1);
    J(s)=J(s-1).*(1-(k(s)).^2);
    
    a(s,s)= -k(s);
    a(1,s)=1;
    for i=2:(s-1),
        a(i,s)=a(i,(s-1)) - k(s).*a((s-i+1),(s-1));
    end
end
%increment "b" and do same for next frame until end of frame when 
%combining this code with other parts of LPC algo


%PREDICTION ERROR; FOR TESTING THE ABOVE PREDICTOR
aCoeff=a((1:s),s)';       %array of "a(i,s)", where, s=M+1
tcount_of_aCoeff = length(aCoeff);

est_y = filter([0 -aCoeff(2:end)],1,y);    % = s^(n) with a cap on page 92 of the book
e = y - est_y;      %supposed to be a white noise