V_TEAGER calculate v_teager energy waveform Y=(X,D,M)
Inputs: x speech signal
d dimension to apply filter along [default 1st non-singleton]
m Normally Y has the same length as X and the first
and last output samples are extrapolated. Setting m='x'
supresses this extrapolation and Y will be two
samples shorter than X
Outputs: Y output signal: y(n)=abs(x(n))^2 - x(n+1)*conj(x(n-1))
Calculates the Teager energy waveform [1]. The following waveforms give
a constant output (independent of n) where A, B, C are real constants:
(a) x(n) = A*sin(B*n+C) --> y(n) = (A*sin(B))^2
(b) x(n) = A*n + B --> y(n) = A^2
(c) x(n) = A*exp(j(B*n+C)) --> y(n) = A^2*(1-exp(2jB))
(d) x(n) = A*exp(B*n+C) --> y(n) = 0
Reference:
[1] J. Kaiser. On a simple algorithm to calculate the "energy" of a signal.
In Proc IEEE Intl Conf Acoustics, Speech and Signal Processing,
pages 381-384, vol.1, Apr. 1990. doi: 10.1109/ICASSP.1990.115702.0001 function y=v_teager(x,d,m) 0002 %V_TEAGER calculate v_teager energy waveform Y=(X,D,M) 0003 % 0004 % Inputs: x speech signal 0005 % d dimension to apply filter along [default 1st non-singleton] 0006 % m Normally Y has the same length as X and the first 0007 % and last output samples are extrapolated. Setting m='x' 0008 % supresses this extrapolation and Y will be two 0009 % samples shorter than X 0010 % 0011 % Outputs: Y output signal: y(n)=abs(x(n))^2 - x(n+1)*conj(x(n-1)) 0012 % 0013 % Calculates the Teager energy waveform [1]. The following waveforms give 0014 % a constant output (independent of n) where A, B, C are real constants: 0015 % (a) x(n) = A*sin(B*n+C) --> y(n) = (A*sin(B))^2 0016 % (b) x(n) = A*n + B --> y(n) = A^2 0017 % (c) x(n) = A*exp(j(B*n+C)) --> y(n) = A^2*(1-exp(2jB)) 0018 % (d) x(n) = A*exp(B*n+C) --> y(n) = 0 0019 % 0020 % Reference: 0021 % [1] J. Kaiser. On a simple algorithm to calculate the "energy" of a signal. 0022 % In Proc IEEE Intl Conf Acoustics, Speech and Signal Processing, 0023 % pages 381-384, vol.1, Apr. 1990. doi: 10.1109/ICASSP.1990.115702. 0024 0025 % Copyright (C) Mike Brookes 1997 0026 % Version: $Id: v_teager.m 10865 2018-09-21 17:22:45Z dmb $ 0027 % 0028 % VOICEBOX is a MATLAB toolbox for speech processing. 0029 % Home page: http://www.ee.ic.ac.uk/hp/staff/dmb/voicebox/voicebox.html 0030 % 0031 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 0032 % This program is free software; you can redistribute it and/or modify 0033 % it under the terms of the GNU General Public License as published by 0034 % the Free Software Foundation; either version 2 of the License, or 0035 % (at your option) any later version. 0036 % 0037 % This program is distributed in the hope that it will be useful, 0038 % but WITHOUT ANY WARRANTY; without even the implied warranty of 0039 % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 0040 % GNU General Public License for more details. 0041 % 0042 % You can obtain a copy of the GNU General Public License from 0043 % http://www.gnu.org/copyleft/gpl.html or by writing to 0044 % Free Software Foundation, Inc.,675 Mass Ave, Cambridge, MA 02139, USA. 0045 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 0046 e=size(x); 0047 p=prod(e); 0048 if nargin<2 % if no dimension given, find the first non-singleton 0049 d=find(e>1,1); 0050 if ~numel(d) 0051 d=1; 0052 end 0053 end 0054 k=e(d); % size of active dimension 0055 q=p/k; % size of remainder 0056 if d==1 0057 z=reshape(x,k,q); 0058 else 0059 z=shiftdim(x,d-1); 0060 r=size(z); 0061 z=reshape(z,k,q); 0062 end 0063 if nargin>2 && any(m=='x') 0064 y=z(2:k-1,:).*conj(z(2:k-1,:))-z(3:k,:).*conj(z(1:k-2,:)); 0065 k=k-2; % we have lost two elements 0066 elseif k>=4 0067 y=zeros(k,q); 0068 y(2:k-1,:)=z(2:k-1,:).*conj(z(2:k-1,:))-z(3:k,:).*conj(z(1:k-2,:)); 0069 y(1,:)=2*y(2,:)-y(3,:); % linearly interpolate the end points 0070 y(k,:)=2*y(k-1,:)-y(k-2,:); 0071 elseif k==3 0072 y=repmat(x(2,:).*conj(x(2,:))-x(3,:).*conj(x(1,:)),3,1); 0073 else 0074 y=zeros(k,q); 0075 end 0076 if d==1 0077 e(d)=k; 0078 y=reshape(y,e); 0079 else 0080 r(1)=k; 0081 y=shiftdim(reshape(y,r),length(e)+1-d); 0082 end