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

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 General Public License as published by 0025 % the Free Software Foundation; either version 2 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 General Public License for more details. 0032 % 0033 % You can obtain a copy of the GNU General Public License from 0034 % http://www.gnu.org/copyleft/gpl.html or by writing to 0035 % Free Software Foundation, Inc.,675 Mass Ave, Cambridge, MA 02139, USA. 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

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