# v_distchpf

## PURPOSE

V_DISTCHPF calculates the cosh spectral distance between power spectra D=(PF1,PF2,MODE)

## SYNOPSIS

function d=v_distchpf(pf1,pf2,mode)

## DESCRIPTION

```V_DISTCHPF calculates the cosh 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 COSH spectral distance is the average over +ve and -ve frequency of

cosh(log(p1/p2))-1   =   (p1-p2)^2/(2p1*p2)   =   (p1/p2 + p2/p1)/2 - 1

The COSH distance is a symmetrical version of the Itakura-Saito distance: v_distchpf(x,y)=(v_distispf(x,y)+v_distispf(y,x))/2```

## CROSS-REFERENCE INFORMATION

This function calls:
This function is called by:

## SOURCE CODE

```0001 function d=v_distchpf(pf1,pf2,mode)
0002 %V_DISTCHPF calculates the cosh 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 COSH spectral distance is the average over +ve and -ve frequency of
0017 %
0018 %                     cosh(log(p1/p2))-1   =   (p1-p2)^2/(2p1*p2)   =   (p1/p2 + p2/p1)/2 - 1
0019 %
0020 % The COSH distance is a symmetrical version of the Itakura-Saito distance: v_distchpf(x,y)=(v_distispf(x,y)+v_distispf(y,x))/2
0021
0022 % The Cosh distance can also be calculated directly from AR coefficients; providing np is large
0023 % enough, the values of d0 and d1 in the following will be very similar:
0024 %
0025 %         np=255; d0=v_distchar(ar1,ar2); d1=v_distchpf(v_lpcar2pf(ar1,np),v_lpcar2pf(ar2,np))
0026 %
0027
0028 % Ref: A.H.Gray Jr and J.D.Markel, "Distance measures for speech processing", IEEE ASSP-24(5): 380-391, Oct 1976
0029 %      L. Rabiner abd B-H Juang, "Fundamentals of Speech Recognition", Section 4.5, Prentice-Hall 1993, ISBN 0-13-015157-2
0030
0031 %      Copyright (C) Mike Brookes 1997
0032 %      Version: \$Id: v_distchpf.m 10865 2018-09-21 17:22:45Z dmb \$
0033 %
0034 %   VOICEBOX is a MATLAB toolbox for speech processing.
0036 %
0037 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
0038 %   This program is free software; you can redistribute it and/or modify
0040 %   the Free Software Foundation; either version 2 of the License, or
0041 %   (at your option) any later version.
0042 %
0043 %   This program is distributed in the hope that it will be useful,
0044 %   but WITHOUT ANY WARRANTY; without even the implied warranty of
0045 %   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
0046 %   GNU General Public License for more details.
0047 %
0048 %   You can obtain a copy of the GNU General Public License from
0049 %   http://www.gnu.org/copyleft/gpl.html or by writing to
0050 %   Free Software Foundation, Inc.,675 Mass Ave, Cambridge, MA 02139, USA.
0051 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
0052
0053 [nf1,p2]=size(pf1);
0054 p1=p2-1;
0055 nf2=size(pf2,1);
0056 if nargin<3 | isempty(mode) mode='0'; end
0057 if any(mode=='d') | (mode~='x' & nf1==nf2)
0058    nx=min(nf1,nf2);
0059    r=pf1(1:nx,:)./pf2(1:nx,:);
0060    q=r+r.^(-1);
0061    d=(2*sum(q(:,2:p1),2)+q(:,1)+q(:,p2))/(4*p1)-1;
0062 else
0063    r=permute(pf1(:,:,ones(1,nf2)),[1 3 2])./permute(pf2(:,:,ones(1,nf1)),[3 1 2]);
0064    q=r+r.^(-1);
0065    d=(2*sum(q(:,:,2:p1),3)+q(:,:,1)+q(:,:,p2))/(4*p1)-1;
0066 end```