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);