% given a speech vector, extracts frames and cepstrum coefficients.
% based on code originally by Laine & Mark, 2002
function ceps = featurize(signal);

al = 160; % 20 ms
ul = 80;  % 10 ms
n = 10;
signal = signal';
frame=signal(1:al);

% evaluate the number of frames and add zeros at the end to ensure that every frame has the same length

N=ceil((length(signal)-ul-1)/ul);
zer=N*ul+al-length(signal);
signal=[signal zeros(1,zer)];

% extract the frames and store them in the matrix frame
for i=1:1:N
    frame=[frame; signal((ul*i+1):(ul*i+al))];
end

a = -real(lpc(frame.',n));

ceps=[]; % initializing h(0) with log(G)=0 (since G=1)
	% calculation of h according to formula 6.119 of the course book
a=a(:,2:size(a,2)); % dropping the first column to get confirm with the notation in the book a(1) belongs now to x[n-1]
for n=1:1:size(a,2)
    summ=zeros(size(a,1),1);  % helpvariable for the sum
    for k=1:1:n-1
        summ=summ+k/n*ceps(:,k).*a(:,n-k);
    end
    ceps=[ceps (a(:,n)+summ)];
end