V_LPCAR2AM Convert ar coefs to ar coef matrix [AM,EM]=(AR,P) 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. EM(:,1) is always 1. 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 For each j in 1:P we have AM(j:end:-1:j+1,*) = AM(j:end-1,end,*)'*am(j+1:end,j+1:end,*) Also em(*,1:end)' = em(*,2:end)'.*(1-am(1:end-1,end,*).^2)
0001 function [am,em]=v_lpcar2am(ar,p); 0002 %V_LPCAR2AM Convert ar coefs to ar coef matrix [AM,EM]=(AR,P) 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 %EM(:,1) is always 1. 0011 % 0012 %If A=am(:,:,*), R=toeplitz(rr(*,:)) and E=diag(em(*,:)), then 0013 % A*R*A'=E; inv(R)=A'*(1/E)*A; A*R is lower triangular with the same diagonal as E 0014 % 0015 % For each j in 1:P we have AM(j:end:-1:j+1,*) = AM(j:end-1,end,*)'*am(j+1:end,j+1:end,*) 0016 % 0017 % Also em(*,1:end)' = em(*,2:end)'.*(1-am(1:end-1,end,*).^2) 0018 0019 % we should be able to do this more directly using the step down algorithm 0020 0021 % Copyright (C) Mike Brookes 1997 0022 % Version: $Id: v_lpcar2am.m 10865 2018-09-21 17:22:45Z dmb $ 0023 % 0024 % VOICEBOX is a MATLAB toolbox for speech processing. 0025 % Home page: http://www.ee.ic.ac.uk/hp/staff/dmb/voicebox/voicebox.html 0026 % 0027 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 0028 % This program is free software; you can redistribute it and/or modify 0029 % it under the terms of the GNU General Public License as published by 0030 % the Free Software Foundation; either version 2 of the License, or 0031 % (at your option) any later version. 0032 % 0033 % This program is distributed in the hope that it will be useful, 0034 % but WITHOUT ANY WARRANTY; without even the implied warranty of 0035 % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 0036 % GNU General Public License for more details. 0037 % 0038 % You can obtain a copy of the GNU General Public License from 0039 % http://www.gnu.org/copyleft/gpl.html or by writing to 0040 % Free Software Foundation, Inc.,675 Mass Ave, Cambridge, MA 02139, USA. 0041 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 0042 0043 [nf,p1] = size(ar); 0044 if any(ar(:,1)~=1) 0045 ar=ar./ar(:,ones(1,p1)); 0046 end 0047 p0=p1-1; 0048 if nargin < 2 0049 p=p0; 0050 end 0051 am=zeros(nf,p+1,p+1); 0052 em=ones(nf,p+1); 0053 e=ones(nf,1); 0054 rf=ar; 0055 if p>=p0 0056 for jj=1:p+1-p0 0057 am(:,jj:jj+p0,jj)=ar; 0058 end 0059 else 0060 for j=p0:-1:p+2 0061 k = rf(:,j+1); 0062 d = (1-k.^2).^(-1); 0063 e = e.*d; 0064 wj=ones(1,j-1); 0065 rf(:,2:j) = (rf(:,2:j)-k(:,wj).*rf(:,j:-1:2)).*d(:,wj); 0066 end 0067 jj=0; 0068 end 0069 for jj=jj+1:p 0070 j = p+2-jj; 0071 k = rf(:,j+1); 0072 d = (1-k.^2).^(-1); 0073 e = e.*d; 0074 wj=ones(1,j-1); 0075 rf(:,2:j) = (rf(:,2:j)-k(:,wj).*rf(:,j:-1:2)).*d(:,wj); 0076 am(:,jj:end,jj)=rf(:,1:j); 0077 em(:,jj)=e; 0078 end 0079 em(:,end)=e./(1-rf(:,2).^2); 0080 am(:,end,end)=1; 0081 am=permute(am,[3 2 1]); 0082