lloyd_max.zip_ lloyd_max_Lloyd_it_lloyd max quantizer_max dct

function [interv,values,probs]=lloyd_max(N) %function y=lloyd_max(N) %Iteratively obtains the optimum (Lloyd-Max) %quantizer for a normally distributed source %(unit variance) and outputs the optimum quantization levels %in vector "interv" and the optimum %quantization values in vector "values". %N is the number of bits of quantization. %It makes use of the fact that the density is symmetric %around zero and only quantizes the positive axis. For the %negative axis, the quantization intervals and values are %the negatives of the ones obtained. % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %Program written for EE 455 by C. Georghiades, Sept. 20, 1998% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %Compute the number of quantization levels, L: L=2^N; %V below is just an initial range and it can be set to any reasonable value. V=2030; %Define initial quantization intervals (uniformly distributed) %teste a=linspace(0,V,L/2); a=[a,0]; %teste %Start the iteration for the Lloyd-Max optimum quantizer: %Use enough the norm of the error for xhat to determine convergence xhat_old=zeros(1,L/2); error=1; while(error>1.0e-6) %Compute the conditional mean estimates, xhat, corresponding to a %(it calls function gauss_distr() which returns the distribution %function of a normal variable): b=gauss_distr(a); c=b(2:length(b))-b(1:length(b)-1); cm=(exp(-a(1:length(a)-1).^2/2)-exp(-a(2:length(a)).^2/2))/sqrt(2*pi); xhat=cm./c; error=norm(xhat-xhat_old); xhat_old=xhat; %Now update a using ai=(xhat_i+xhat_(i+1))/2: a1=(xhat(2:length(xhat))+xhat(1:length(xhat)-1))/2; %Append the boundaries of the quantization interval a=[0,a1,Inf]; end interv=a; values=xhat; probs=c;