function [pf,f]=v_lpcar2pf(ar,np)
%V_LPCAR2PF Convert AR coefs to power spectrum PF=(AR,NP)
%
%  Inputs: ar(nf,n)     AR coefficients, one frame per row
%          np           Size of output spectrum is np+1 [n]
%
% Outputs: pf(nf,np+1)  Power spectrum from DC to Nyquist
%          f(1,np+1)    Normalized frequencies (0 to 0.5)
%
% For high speed make np equal to a power of 2

%      Copyright (C) Mike Brookes 1998-2014
%      Version: $Id: v_lpcar2pf.m 10865 2018-09-21 17:22:45Z dmb $
%
%   VOICEBOX is a MATLAB toolbox for speech processing.
%   Home page: http://www.ee.ic.ac.uk/hp/staff/dmb/voicebox/voicebox.html
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%   This program is free software; you can redistribute it and/or modify
%   it under the terms of the GNU General Public License as published by
%   the Free Software Foundation; either version 2 of the License, or
%   (at your option) any later version.
%
%   This program is distributed in the hope that it will be useful,
%   but WITHOUT ANY WARRANTY; without even the implied warranty of
%   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
%   GNU General Public License for more details.
%
%   You can obtain a copy of the GNU General Public License from
%   http://www.gnu.org/copyleft/gpl.html or by writing to
%   Free Software Foundation, Inc.,675 Mass Ave, Cambridge, MA 02139, USA.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

[nf,p1]=size(ar);
if nargin<2
    if nargout
        np=p1-1;
    else
        np=128;
    end
end
pf=abs(v_rfft(ar.',2*np).').^(-2);
f=(0:np)/(2*np);
if ~nargout
        plot(f,pf.');
        xlabel('Normalized frequency f/f_s');
        ylabel('LPC Power Spectrum');
end

