V_LPCAR2RF Convert autoregressive coefficients to formant freq+amp+bw [N,F,A,B]=(AR,T)
Input: ar(:,p+1) Autoregressive coefficients
t Threshold (see below)
Output: n Number of formants found
f Formant frequencies in normalized Hz (in increasing order)
a Formant amplitudes
b Formant bandwidths in normalized Hz
The number of columns in the output arrays f, a and b is max(n); surplus positions
in any given row have f=b=0.
In determining formants, poles are ignored if any of the following hold:
(a) they are on the real axis
(b) they have bandwidth > t*frequency (if t>0)
(c) they have bandwidth > -t (if t<=0)0001 function [n,f,a,b]=v_lpcar2fm(ar,t) 0002 %V_LPCAR2RF Convert autoregressive coefficients to formant freq+amp+bw [N,F,A,B]=(AR,T) 0003 % 0004 % Input: ar(:,p+1) Autoregressive coefficients 0005 % t Threshold (see below) 0006 % Output: n Number of formants found 0007 % f Formant frequencies in normalized Hz (in increasing order) 0008 % a Formant amplitudes 0009 % b Formant bandwidths in normalized Hz 0010 % 0011 % The number of columns in the output arrays f, a and b is max(n); surplus positions 0012 % in any given row have f=b=0. 0013 % 0014 % In determining formants, poles are ignored if any of the following hold: 0015 % (a) they are on the real axis 0016 % (b) they have bandwidth > t*frequency (if t>0) 0017 % (c) they have bandwidth > -t (if t<=0) 0018 0019 % Copyright (C) Mike Brookes 1997 0020 % Version: $Id: v_lpcar2fm.m 10865 2018-09-21 17:22:45Z dmb $ 0021 % 0022 % VOICEBOX is a MATLAB toolbox for speech processing. 0023 % Home page: http://www.ee.ic.ac.uk/hp/staff/dmb/voicebox/voicebox.html 0024 % 0025 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 0026 % This program is free software; you can redistribute it and/or modify 0027 % it under the terms of the GNU General Public License as published by 0028 % the Free Software Foundation; either version 2 of the License, or 0029 % (at your option) any later version. 0030 % 0031 % This program is distributed in the hope that it will be useful, 0032 % but WITHOUT ANY WARRANTY; without even the implied warranty of 0033 % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 0034 % GNU General Public License for more details. 0035 % 0036 % You can obtain a copy of the GNU General Public License from 0037 % http://www.gnu.org/copyleft/gpl.html or by writing to 0038 % Free Software Foundation, Inc.,675 Mass Ave, Cambridge, MA 02139, USA. 0039 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 0040 0041 [nf,p1]=size(ar); 0042 p=p1-1; 0043 d=(1:nf)'; 0044 zz=v_lpcar2zz(ar); 0045 ig=imag(zz)<=0; 0046 n=p1-1-sum(ig,2); 0047 mn=max(n); 0048 0049 % remove redundant columns 0050 0051 if mn<p 0052 [ig,ix]=sort(ig,2); 0053 zz=reshape(zz(d(:,ones(1,mn))+nf*(ix(:,1:mn)-1)),nf,mn); 0054 ig(:,mn+1:end)=[]; 0055 end 0056 0057 zz(ig)=1; % to prevent infinities 0058 f=angle(zz)*0.5/pi; 0059 b=-log(abs(zz))/pi; 0060 if nargin > 1 0061 if t>0 0062 ig=ig | b>t*f; 0063 else 0064 ig=ig | b+t>0; 0065 end 0066 end 0067 f(ig)=0; 0068 b(ig)=0; 0069 n=mn-sum(ig,2); 0070 m=max(n); 0071 0072 % remove redundant columns 0073 0074 [igf,ix]=sort(ig+f,2); 0075 dd=d(:,ones(1,m))+nf*(ix(:,1:m)-1); 0076 zz=reshape(zz(dd),nf,m); 0077 f=reshape(f(dd),nf,m); 0078 b=reshape(b(dd),nf,m); 0079 ig=reshape(ig(dd),nf,m); 0080 0081 % now calculate gain 0082 ap=permute(ar,[1 3 2]); 0083 pw=permute(-2*pi*1i*(0:p),[1 3 2]); 0084 a=abs(sum(ap(:,ones(1,m),:).*exp(pw(ones(1,nf),ones(1,m),:).*f(:,:,ones(1,p1))),3)).^(-1);