V_DISTISPF calculates the Itakura-Saito spectral distance between power spectra D=(PF1,PF2,MODE) Inputs: PF1,PF2 Power spectra to be compared. Each row represents a power spectrum: the first and last columns represent the DC and Nyquist terms respectively. PF1 and PF2 must have the same number of columns. MODE Character string selecting the following options: 'x' Calculate the full distance matrix from every row of PF1 to every row of PF2 'd' Calculate only the distance between corresponding rows of PF1 and PF2 The default is 'd' if PF1 and PF2 have the same number of rows otherwise 'x'. Output: D If MODE='d' then D is a column vector with the same number of rows as the shorter of PF1 and PF2. If MODE='x' then D is a matrix with the same number of rows as PF1 and the same number of columns as PF2'. The Itakura-Saito spectral distance is the average over +ve and -ve frequency of pf1/pf2 - log(pf1/pf2) - 1 = exp(v) - v - 1 where v=log(pf1/pf2) The Itakura-Saito distance is asymmetric: pf1>pf2 contributes more to the distance than pf2>pf1. A symmetrical version is the COSH distance: v_distchpf(x,y)=(v_distispf(x,y)+v_distispf(y,x))/2

0001 function d=v_distispf(pf1,pf2,mode) 0002 %V_DISTISPF calculates the Itakura-Saito spectral distance between power spectra D=(PF1,PF2,MODE) 0003 % 0004 % Inputs: PF1,PF2 Power spectra to be compared. Each row represents a power spectrum: the first 0005 % and last columns represent the DC and Nyquist terms respectively. 0006 % PF1 and PF2 must have the same number of columns. 0007 % 0008 % MODE Character string selecting the following options: 0009 % 'x' Calculate the full distance matrix from every row of PF1 to every row of PF2 0010 % 'd' Calculate only the distance between corresponding rows of PF1 and PF2 0011 % The default is 'd' if PF1 and PF2 have the same number of rows otherwise 'x'. 0012 % 0013 % Output: D If MODE='d' then D is a column vector with the same number of rows as the shorter of PF1 and PF2. 0014 % If MODE='x' then D is a matrix with the same number of rows as PF1 and the same number of columns as PF2'. 0015 % 0016 % The Itakura-Saito spectral distance is the average over +ve and -ve frequency of 0017 % 0018 % pf1/pf2 - log(pf1/pf2) - 1 = exp(v) - v - 1 where v=log(pf1/pf2) 0019 % 0020 % The Itakura-Saito distance is asymmetric: pf1>pf2 contributes more to the distance than pf2>pf1. 0021 % A symmetrical version is the COSH distance: v_distchpf(x,y)=(v_distispf(x,y)+v_distispf(y,x))/2 0022 0023 % The Itakura-Saito distance can also be calculated directly from AR coefficients; providing np is large 0024 % enough, the values of d0 and d1 in the following will be very similar: 0025 % 0026 % np=255; d0=v_distisar(ar1,ar2); d1=v_distispf(v_lpcar2pf(ar1,np),v_lpcar2pf(ar2,np)) 0027 % 0028 0029 % Ref: A.H.Gray Jr and J.D.Markel, "Distance measures for speech processing", IEEE ASSP-24(5): 380-391, Oct 1976 0030 % L. Rabiner abd B-H Juang, "Fundamentals of Speech Recognition", Section 4.5, Prentice-Hall 1993, ISBN 0-13-015157-2 0031 % F.Itakura & S.Saito, "A statistical method for estimation of speech spectral density and formant frequencies", 0032 % Electronics & Communications in Japan, 53A: 36-43, 1970. 0033 0034 0035 % Copyright (C) Mike Brookes 1997 0036 % Version: $Id: v_distispf.m 10865 2018-09-21 17:22:45Z dmb $ 0037 % 0038 % VOICEBOX is a MATLAB toolbox for speech processing. 0039 % Home page: http://www.ee.ic.ac.uk/hp/staff/dmb/voicebox/voicebox.html 0040 % 0041 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 0042 % This program is free software; you can redistribute it and/or modify 0043 % it under the terms of the GNU General Public License as published by 0044 % the Free Software Foundation; either version 2 of the License, or 0045 % (at your option) any later version. 0046 % 0047 % This program is distributed in the hope that it will be useful, 0048 % but WITHOUT ANY WARRANTY; without even the implied warranty of 0049 % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 0050 % GNU General Public License for more details. 0051 % 0052 % You can obtain a copy of the GNU General Public License from 0053 % http://www.gnu.org/copyleft/gpl.html or by writing to 0054 % Free Software Foundation, Inc.,675 Mass Ave, Cambridge, MA 02139, USA. 0055 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 0056 0057 [nf1,p2]=size(pf1); 0058 p1=p2-1; 0059 nf2=size(pf2,1); 0060 if nargin<3 | isempty(mode) mode='0'; end 0061 if any(mode=='d') | (mode~='x' & nf1==nf2) 0062 nx=min(nf1,nf2); 0063 r=pf1(1:nx,:)./pf2(1:nx,:); 0064 q=r-log(r); 0065 d=(sum(q(:,2:p1),2)+0.5*(q(:,1)+q(:,p2)))/p1-1; 0066 else 0067 r=permute(pf1(:,:,ones(1,nf2)),[1 3 2])./permute(pf2(:,:,ones(1,nf1)),[3 1 2]); 0068 q=r-log(r); 0069 d=(sum(q(:,:,2:p1),3)+0.5*(q(:,:,1)+q(:,:,p2)))/p1-1; 0070 end

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