# v_lpcrf2ar

## PURPOSE

V_LPCRF2AR Convert reflection coefs to autoregressive coefs [AR,ARP,ARU,G]=(RF)

## SYNOPSIS

function [ar,arp,aru,g]=v_lpcrf2ar(rf)

## DESCRIPTION

    V_LPCRF2AR Convert reflection coefs to autoregressive coefs [AR,ARP,ARU,G]=(RF)

     Input:  RF(:,p+1) gives reflection coefficients of one or more p-section lossless tubes
     Ouputs: G is the gain of the all-pole AR filter
             AR/G is the transfer function from U_in to the glottal input wave, U_g.
                   AR(:,1)=1 always.
             ARP*K is the transfer function from U_in to the pressure just after the glottis
                   where K = rho*c/Alips: rho = air density 1.23 kg/m^3, c=sound speed 340 m/s,
                   Alips = effective area of free space beyond the lips.
             ARU is the transfer function from U_in to the total volume velocity through the glottis

                  where U_in=z^(p/2)*U_lips is the time-advanced volume velocity at the lips

             Energy into the vcal tract is equal to K*filter(ARP,1,Ulips).*filter(ARU,1,Ulips)
                  reverse glottal flows divided by 1-r0 where r0 is the glottal reflection coefficient.
                  The scale factor is included to avoid a zero answer when the glottis is closed giving r0=1.

     The transfer functions have ar(:,1)=art(:,1)=1
     They should both be multiplied by z^(p/2)/prod(1+rf) to correct the absolute
     gain and to compensate for the delay of p/2 samples along the length of the tube.

     The energy into the vocal tract is given by ars(speech) * are(speech)

     Ref: D. M. Brookes and H. P. Loke. "Modelling energy flow in the vocal tract with
               applications to glottal closure and opening detection." In Proc ICASSP'99, pages 213-216, Mar 1999.

## CROSS-REFERENCE INFORMATION

This function calls:

This function is called by:

- v_lpcrand V_LPCRAND generate random stable polynomials AR=(P,N,BW)

## SOURCE CODE

    0001 function [ar,arp,aru,g]=v_lpcrf2ar(rf)
    0002 %V_LPCRF2AR Convert reflection coefs to autoregressive coefs [AR,ARP,ARU,G]=(RF)
    0003 %
    0004 % Input:  RF(:,p+1) gives reflection coefficients of one or more p-section lossless tubes
    0005 % Ouputs: G is the gain of the all-pole AR filter
    0006 %         AR/G is the transfer function from U_in to the glottal input wave, U_g.
    0007 %               AR(:,1)=1 always.
    0008 %         ARP*K is the transfer function from U_in to the pressure just after the glottis
    0009 %               where K = rho*c/Alips: rho = air density 1.23 kg/m^3, c=sound speed 340 m/s,
    0010 %               Alips = effective area of free space beyond the lips.
    0011 %         ARU is the transfer function from U_in to the total volume velocity through the glottis
    0012 %
    0013 %              where U_in=z^(p/2)*U_lips is the time-advanced volume velocity at the lips
    0014 %
    0015 %         Energy into the vcal tract is equal to K*filter(ARP,1,Ulips).*filter(ARU,1,Ulips)
    0016 %              reverse glottal flows divided by 1-r0 where r0 is the glottal reflection coefficient.
    0017 %              The scale factor is included to avoid a zero answer when the glottis is closed giving r0=1.
    0018 %
    0019 % The transfer functions have ar(:,1)=art(:,1)=1
    0020 % They should both be multiplied by z^(p/2)/prod(1+rf) to correct the absolute
    0021 % gain and to compensate for the delay of p/2 samples along the length of the tube.
    0022 %
    0023 % The energy into the vocal tract is given by ars(speech) * are(speech)
    0024 %
    0025 % Ref: D. M. Brookes and H. P. Loke. "Modelling energy flow in the vocal tract with
    0026 %           applications to glottal closure and opening detection." In Proc ICASSP'99, pages 213-216, Mar 1999.
    0027
    0028
    0029 %      Copyright (C) Mike Brookes 1997
    0030 %      Version: $Id: v_lpcrf2ar.m 10865 2018-09-21 17:22:45Z dmb $
    0031 %
    0032 %   VOICEBOX is a MATLAB toolbox for speech processing.
    0033 %   Home page: http://www.ee.ic.ac.uk/hp/staff/dmb/voicebox/voicebox.html
    0034 %
    0035 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    0036 %   This program is free software; you can redistribute it and/or modify
    0037 %   it under the terms of the GNU Lesser General Public License as published by
    0038 %   the Free Software Foundation; either version 3 of the License, or
    0039 %   (at your option) any later version.
    0040 %
    0041 %   This program is distributed in the hope that it will be useful,
    0042 %   but WITHOUT ANY WARRANTY; without even the implied warranty of
    0043 %   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
    0044 %   GNU Lesser General Public License for more details.
    0045 %
    0046 %   You can obtain a copy of the GNU Lesser General Public License from
    0047 %   https://www.gnu.org/licenses/ .
    0048 %
    0049 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    0050
    0051 [nf,p1]=size(rf);
    0052 p2=p1+1;
    0053 p=p1-1;
    0054 pm=p-1;
    0055 arf=[ones(nf,1) zeros(nf,p)];
    0056 arr=[zeros(nf,p) rf(:,p1)];
    0057 cr=zeros(nf,p);
    0058 for k=1:p-1
    0059   rk=rf(:,(p1-k)*ones(1,k));
    0060   cr(:,1:k)=arr(:,p2-k:p1);
    0061   arr(:,p1-k:p)=arr(:,p1-k:p)+rk.*arf(:,1:k);
    0062   arf(:,2:k+1)=arf(:,2:k+1)+rk.*cr(:,1:k);
    0063 end
    0064 r1=rf(:,1);
    0065 ar=arf+r1(:,ones(1,p1)).*arr;
    0066 if nargout>1
    0067    kp=prod(1-rf(:,2:p1),2);
    0068    arp=(arf-arr)./kp(:,ones(1,p1));
    0069    if nargout>2
    0070       g=prod(1+rf(:,2:p1),2);
    0071       aru=(arf+arr)./g(:,ones(1,p1));
    0072       if nargout>3
    0073          g=g.*(1+rf(:,1));
    0074       end
    0075    end
    0076 end
    0077
    0078