function [k,P0] = stepdown(a,PM)
% Direct form to Lattice (step-down) Conversion
% --------------------------------------
% [k,P0] = stepdown(a,PM)
%  k = Lattice filter coefficients (reflection coefficients)
% P0 = Initial error variance
%  a = direct form coefficients (impulse response)
% PM = Final error Variance
%
%-----------------------------------------------------------
% Copyright 2000, by Dimitris G. Manolakis, Vinay K. Ingle,
% and Stephen M. Kogon.  For use with the book
% "Statistical and Adaptive Signal Processing"
% McGraw-Hill Higher Education.
%-----------------------------------------------------------


% Initialization
P = PM;
M = length(a);
k = zeros(M,1);

% Recursion
for m = M:-1:2
   k(m) = a(m); den = (1-k(m)*conj(k(m)));
   a = a(1:m-1);
   a = (a - flipud(conj(a))*k(m))/den;
   P = P/den;
end
k(1) = a(1);
P0 = P/(1-k(1)*conj(k(1)));