function astar=smooth_a(a,gama);
% Syntax: astar=smooth_a(a,gama);
% 
% function for smoothing the response of synthesis filter 1/A(z)
% a is the vector of prediction coefficients [1 a1 a2 ... aP],
%    of length P+1, where P is the prediction order.
% astar are coefficients of filter 1/A*(z), obtained
%    from 1/A(z) by substitution z^(-1)--->gama z^(-1)
% gama (optional) is the "smoothening factor", default 0.996
%
% The effect of this function is deplacing of the poles from the unity circle.
% If the poles are to too concentrated, one can approximate
% the minimum bandwidth of a max. introduces by a pole by:
%      B=1/pi * Fe * (1-gama)
% for gama=0.996 and Fe=8000Hz, B=10Hz

if (nargin == 1),
  gama=0.996;
end

P=length(a)-1;

powers=(0:P)';
factors=gama*ones(size(a)) .^ powers;
astar = a.*factors;