function [mobility,complexity] = HjorthParameters(xV)
% [mobility,complexity] = HjorthParameters(xV)
% HJORTHPARAMETERS computes the Hjorth parameters mobility and complexity.
% INPUTS:
% - xV : The given scalar time series (vector of size n x 1).
% OUTPUTS
% - mobility
%========================================================================
% <HjorthParameters.m>, v 1.0 2010/02/11 22:09:14 Kugiumtzis & Tsimpiris
% This is part of the MATS-Toolkit http://eeganalysis.web.auth.gr/
%========================================================================
% Copyright (C) 2010 by Dimitris Kugiumtzis and Alkiviadis Tsimpiris
% <dkugiu@gen.auth.gr>
%========================================================================
% Version: 1.0
% LICENSE:
% 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 3 of the License, or
% 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.
%
% You should have received a copy of the GNU General Public License
% along with this program. If not, see http://www.gnu.org/licenses/>.
%=========================================================================
% Reference : D. Kugiumtzis and A. Tsimpiris, "Measures of Analysis of Time Series (MATS):
% A Matlab Toolkit for Computation of Multiple Measures on Time Series Data Bases",
% Journal of Statistical Software, in press, 2010
% Link : http://eeganalysis.web.auth.gr/
%=========================================================================
n = length(xV);
dxV = diff([0;xV]);
ddxV = diff([0;dxV]);
mx2 = mean(xV.^2);
mdx2 = mean(dxV.^2);
mddx2 = mean(ddxV.^2);
mob = mdx2 / mx2;
complexity = sqrt(mddx2 / mdx2 - mob);
mobility = sqrt(mob);