function plot_a_lsf(a,f);
% Syntax: plot_a_lsf(a,f)
%
% Function for plotting of LPC and LSF.
% a is the vector of LPC coefficients [1 a1 ... aP]  - size P+1
% f is the vector of Line Spectrum Frequencies (LSF) - size P
% Two plots are produced 
%  - normalized module of LPC spectrum with LSFs belonging 
%     to polynomial P (green) and Q (red)
%  - roots of P (green) and of Q (red)
% a and f are COLUMN vectors.

M=length(a)-1;
if length(f) ~= M
  error ('The length of vector a must be the length of f plus one');
end
  
a=[a; 0];
p=a-a(M+2:-1:1);
q=a+a(M+2:-1:1);

rp=roots(p);
rq=roots(q);

figure(1);				% roots in z-plane
polar(angle(rp), abs(rp), 'og');	% P
hold on
polar(angle(rq), abs(rq), 'or');	% Q
hold off
title ('P - green, Q - red');

figure(2);				% LPC spec + frequencies.
hold off;
if (M/2)==floor(M/2),		% M even - P and Q have the same no. of freq.
				% Q begins.
  fq=f(1:2:M-1); 		% Q will have the 1st freq from f
  fp=f(2:2:M);   		% P will have the 2nd 
  noP=M/2; noQ=M/2;		% numbers
else				% M odd - Q will have 1 more freq. than P	
  fq=f(1:2:M); 			% Q will have the 1st freq from f
  fp=f(2:2:M-1);  		% P has less
  noP=(M+1)/2-1;  noQ=(M+1)/2;
end

f=(0:511)/1024;
H=abs(freqz(1,a,512));
maxH=max(H);
plot(f,H,'y'); hold on;		% spec in yellow

%cannot make colors - stupisd !stem(fp,maxH*ones(noP,1),'g');  % P in green
%stem(fq,maxH*ones(noQ,1),'r');  % Q in red

for i=1:noP, plot([fp fp],[0,maxH],'g'); end
for i=1:noQ, plot([fq fq],[0,maxH],'r'); end
hold off
title ('LPC spec. - yellow, P - green. Q - red');