function [TKenergy]=TKEO(x)

%

%% Utility function to calculate measures based on the nonlinear energy operator

%

% Function to estimate the TKEO of input data, follows the classical rule

% of Teager and Kaiser

%

% Inputs:  x            -> any time-series signal (vector)

%

% =========================================================================

% Output:  TKenergy     -> (nonlinear) Teager-Kaiser Energy Operator (TKEO)

% =========================================================================

%

% Part of the "Speech Disorders" Toolbox

%

% -----------------------------------------------------------------------

% Useful references:

% 

% 1) J. Kaiser: On a simple algorithm to calculate the 'energy' of a

%    signal, Proc. IEEE International Conference on Acoustics, Speech, and 

%    Signal Processing (ICASSP '90), pp. 381-384, Albuquerque, NM, USA, 

%    April 1990

%

% -----------------------------------------------------------------------

%

% Last modified on 24 August 2014

%

% Copyright (c) Athanasios Tsanas, 2014

%

% ********************************************************************

% If you use this program please cite:

%

% 1) A. Tsanas: "Accurate telemonitoring of Parkinson's disease symptom

%    severity using nonlinear speech signal processing and statistical

%    machine learning", D.Phil. thesis, University of Oxford, 2012

% ********************************************************************

%

% For any question, to report bugs, or just to say this was useful, email

% tsanasthanasis@gmail.com

%% Algorithm computation

% The algorithm is computed using the instantaneous value squared minus the

% previous step value times the next step value:[x_n]^2-[x_(n-1)]*(x_(n+1)]

%

%

% This program is free software; you can redistribute it and/or modify it

% under the terms of the GNU General Public License as published by the

% Free Software Foundation; either version 2 of the License, or (at your

% option) any later version.

% This program is distributed in the hope that it will be useful, but

% WITHOUT ANY WARRANTY; without even the implied warranty of

% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General

% Public License for more details.

% This program is free software; you can redistribute it and/or modify it

% under the terms of the GNU General Public License as published by the

% Free Software Foundation; either version 2 of the License, or (at your

% option) any later version.

% This program is distributed in the hope that it will be useful, but

% WITHOUT ANY WARRANTY; without even the implied warranty of

% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General

% Public License for more details.

%

data_length=length(x);

TKenergy=zeros(data_length,1);

TKenergy(1)=(x(1))^2; % first sample

for n=2:data_length-1

    TKenergy(n)=(x(n))^2-x(n-1)*x(n+1);

end

%  TKenergy(2:data_length-1) = x(2:data_length-1).^2 - x(1:data_length-2).*x(3:data_length); % alternative, vectorized version

TKenergy(data_length)=(x(data_length))^2; % last sample