# v_ewgrpdel

## PURPOSE V_EWGRPDEL calculates the energy weighted group delay waveform Y=(X,W,M)

## SYNOPSIS function [y,mm]=v_ewgrpdel(x,w,m)

## DESCRIPTION ```V_EWGRPDEL calculates the energy weighted group delay waveform Y=(X,W,M)
For each sample, x(n), this routine calculates the energy-weighted average
group delay over frequency using a window centred on x(n). This is equal to
the delay from the window centre to the centre of gravity of energy in the window.

Inputs: x    is the input signal
w    is the window (or just the length of a Hamming window)
m    is the sample of w to use as the centre [default=(length(w)+1)/2]

mm   the actual value of m used. Output point y(i) is based on x(i+m-w:i+m-1).

If w is odd and m has its default value, then an impulse at x(i) will
result in a negative-going zero crossing at y(i). More generally, if the
window is symmetrical it will result in a negative-going zero crossing at
y(i+m-(w+1)/2).```

## CROSS-REFERENCE INFORMATION This function calls:
This function is called by:

## SOURCE CODE ```0001 function [y,mm]=v_ewgrpdel(x,w,m)
0002 %V_EWGRPDEL calculates the energy weighted group delay waveform Y=(X,W,M)
0003 % For each sample, x(n), this routine calculates the energy-weighted average
0004 % group delay over frequency using a window centred on x(n). This is equal to
0005 % the delay from the window centre to the centre of gravity of energy in the window.
0006 %
0007 % Inputs: x    is the input signal
0008 %         w    is the window (or just the length of a Hamming window)
0009 %         m    is the sample of w to use as the centre [default=(length(w)+1)/2]
0010 %
0011 %         mm   the actual value of m used. Output point y(i) is based on x(i+m-w:i+m-1).
0012 %
0013 % If w is odd and m has its default value, then an impulse at x(i) will
0014 % result in a negative-going zero crossing at y(i). More generally, if the
0015 % window is symmetrical it will result in a negative-going zero crossing at
0016 % y(i+m-(w+1)/2).
0017
0018 % Example: x=zeros(1000,1); x(100:100:900)=1; v_ewgrpdel(x,99);
0019
0020 %       Copyright (C) Mike Brookes 2003
0021 %      Version: \$Id: v_ewgrpdel.m 10865 2018-09-21 17:22:45Z dmb \$
0022 %
0023 %   VOICEBOX is a MATLAB toolbox for speech processing.
0025 %
0026 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
0027 %   This program is free software; you can redistribute it and/or modify
0029 %   the Free Software Foundation; either version 2 of the License, or
0030 %   (at your option) any later version.
0031 %
0032 %   This program is distributed in the hope that it will be useful,
0033 %   but WITHOUT ANY WARRANTY; without even the implied warranty of
0034 %   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
0035 %   GNU General Public License for more details.
0036 %
0037 %   You can obtain a copy of the GNU General Public License from
0038 %   http://www.gnu.org/copyleft/gpl.html or by writing to
0039 %   Free Software Foundation, Inc.,675 Mass Ave, Cambridge, MA 02139, USA.
0040 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
0041
0042 if nargin < 2
0043    w=hamming(length(x));
0044 elseif  length(w)==1
0045    w=hamming(w);
0046 end
0047 w=w.^2;
0048 lw=length(w);
0049 if nargin < 3
0050    m=(1+lw)/2;
0051 end
0052 m=max(round(m),1);
0053 mm=m;
0054 wn=w(:).*(m-(1:lw))';
0055 x2=[x(:); zeros(m-1,1)].^2;
0056 yn=filter(wn,1,x2);
0057 yd=filter(w,1,x2);
0058 yd(yd<eps)=1;
0059 y=yn(m:end)./yd(m:end);
0060 if nargout==0
0061    plot(y);
0062    hold on;
0063    plot(x,'r');
0064    hold off;
0065 end```