# v_lpcrr2am

## PURPOSE

V_LPCRR2AM Convert autocorrelation coefs to ar coef matrix [AM,EM]=(RR)

## SYNOPSIS

function [am,em]=v_lpcrr2am(rr);

## DESCRIPTION

    V_LPCRR2AM Convert autocorrelation coefs to ar coef matrix [AM,EM]=(RR)
    AM is a 3-dimensional matrix of size (p+1,p+1,nf) where p is the lpc order
    and nf the number of frames.
    The matrix AM(:,:,*) is upper triangular with 1's on the main diagonal
    and contains the lpc coefficients for all orders from p down to 0.

    For lpc order p+1-r, AM(r,r:p+1,*), AM(p+1:-1:r,p+1,*) and EM(*,r) contain
    the lpc coefficients, reflection coefficients and the residual energy respectively.

    If A=am(:,:,*), R=toeplitz(rr(*,:)) and E=diag(em(*,:)), then
     A*R*A'=E; inv(R)=A'*(1/E)*A; A*R is lower triangular with the same diagonal as E

     This routine is equivalent to: c=chol(inv(toeplitz(rr))); d=diag(c).^-1; em=d.^2; am=diag(d)*c

## CROSS-REFERENCE INFORMATION

This function calls:

This function is called by:

## SOURCE CODE

    0001 function [am,em]=v_lpcrr2am(rr);
    0002 %V_LPCRR2AM Convert autocorrelation coefs to ar coef matrix [AM,EM]=(RR)
    0003 %AM is a 3-dimensional matrix of size (p+1,p+1,nf) where p is the lpc order
    0004 %and nf the number of frames.
    0005 %The matrix AM(:,:,*) is upper triangular with 1's on the main diagonal
    0006 %and contains the lpc coefficients for all orders from p down to 0.
    0007 %
    0008 %For lpc order p+1-r, AM(r,r:p+1,*), AM(p+1:-1:r,p+1,*) and EM(*,r) contain
    0009 %the lpc coefficients, reflection coefficients and the residual energy respectively.
    0010 %
    0011 %If A=am(:,:,*), R=toeplitz(rr(*,:)) and E=diag(em(*,:)), then
    0012 % A*R*A'=E; inv(R)=A'*(1/E)*A; A*R is lower triangular with the same diagonal as E
    0013 %
    0014 % This routine is equivalent to: c=chol(inv(toeplitz(rr))); d=diag(c).^-1; em=d.^2; am=diag(d)*c
    0015
    0016 %      Copyright (C) Mike Brookes 1997
    0017 %      Version: $Id: v_lpcrr2am.m 10865 2018-09-21 17:22:45Z dmb $
    0018 %
    0019 %   VOICEBOX is a MATLAB toolbox for speech processing.
    0020 %   Home page: http://www.ee.ic.ac.uk/hp/staff/dmb/voicebox/voicebox.html
    0021 %
    0022 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    0023 %   This program is free software; you can redistribute it and/or modify
    0024 %   it under the terms of the GNU Lesser General Public License as published by
    0025 %   the Free Software Foundation; either version 3 of the License, or
    0026 %   (at your option) any later version.
    0027 %
    0028 %   This program is distributed in the hope that it will be useful,
    0029 %   but WITHOUT ANY WARRANTY; without even the implied warranty of
    0030 %   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
    0031 %   GNU Lesser General Public License for more details.
    0032 %
    0033 %   You can obtain a copy of the GNU Lesser General Public License from
    0034 %   https://www.gnu.org/licenses/ .
    0035 %
    0036 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
    0037
    0038 [nf,p1]=size(rr);
    0039 p=p1-1;
    0040 p2=p1+1;
    0041 am=zeros(nf,p1,p1);
    0042 em=zeros(nf,p1);
    0043 am(:,p1,p1)=1;
    0044 em(:,p1)=rr(:,1);
    0045 ar=ones(nf,p1);
    0046 ar(:,2) = -rr(:,2)./rr(:,1);
    0047 e = rr(:,1).*(ar(:,2).^2-1);
    0048 for n = 2:p
    0049    q=p2-n;
    0050    em(:,q)=-e;
    0051    am(:,q:p1,q)=ar(:,1:n);
    0052    k = (rr(:,n+1)+sum(rr(:,n:-1:2).*ar(:,2:n),2)) ./ e;
    0053    ar(:,2:n) = ar(:,2:n)+k(:,ones(1,n-1)).*ar(:,n:-1:2);
    0054    ar(:,n+1) = k;
    0055    e = e.*(1-k.^2);
    0056 end
    0057 em(:,1)=-e;
    0058 am(:,:,1)=ar;
    0059 am=permute(am,[3 2 1]);
    0060