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−function   varargout = ltpda_series_derivative(varargin)
+
−%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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−%
+
−% DESCRIPTION: LTPDA_SERIES_DERIVATIVE performs the numeric time derivative
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−% using the method of five points stencil Taylor series expansion [1].
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−% The function can perform the first, second, third and fourth derivetive
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−% of a series of input data.
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−% 
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−%
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−%
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−% CALL:                 Deriv = ltpda_series_derivative(a, ... , pl)
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−%                      
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−%
+
−% INPUTS:      
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−%           - Aos containing the data to be differentiated.
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−%           - pl: is a parameter list containing the options for the
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−%           calculation. Parameters are:
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−%           - 'ORDER' whose accepeted options are:
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−%               - 'FIRST' perform the first derivative using the
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−%               couefficients vector d1 = [1 -8 0 8 -1]./(12*T)
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−%               - 'SECOND' perform the second derivative using the
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−%               coefficients vector d2 = [-1 16 -30 16 -1]./(12*T^2)
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−%               - 'THIRD' perform the third derivative using the
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−%               coefficients vector d3 = [-1 2 0 -2 1]./(2*T^3)
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−%               - 'FOURTH' perform the third derivative using the
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−%               coefficients vector d4 = [1 -4 6 -4 1]./(T^4)
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−%                
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−%           NOTE1: T is the sampling period
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−%           NOTE2: The default option for 'ORDER' is 'SECOND'
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−%              
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−%
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−%
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−% OUTPUTS:     
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−%           - Deriv is avector containing the resulting Aos after
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−%           differentiation
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−% 
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−% 
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−% REFERENCES:
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−%           [1] S. E. Koonin and D. C. Meredith, COMPUTATIONAL PHYSICS -
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−%           Fortran Version, 1990, Westview Press
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−%
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−%
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−% VERSION:     $Id: ltpda_series_derivative.m,v 1.1 2008/04/24 16:13:12 luigi Exp $
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−% 
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−% HISTORY:     18-03-2008 L Ferraioli
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−%                 Creation
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−%
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−% The following call returns a parameter list object that contains the
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−% default parameter values:
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−%
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−% >> pl = ltpda_series_derivative('Params')
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−%
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−% The following call returns a string that contains the routine CVS version:
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−%
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−% >> version = ltpda_series_derivative('Version')
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−%
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−% The following call returns a string that contains the routine category:
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−%
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−% >> category = ltpda_series_derivative('Category')
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−%
+
−%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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−
+
−
+
−
+
−%% Standard history variables
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−
+
−ALGONAME = mfilename;
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−VERSION  = '$Id: ltpda_series_derivative.m,v 1.1 2008/04/24 16:13:12 luigi Exp $';
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−CATEGORY = 'Signal Processing';
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−
+
−%% Check if this is a call for parameters, the CVS version string
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−% or the method category
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−if nargin == 1 && ischar(varargin{1})
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−  in = char(varargin{1});
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−  if strcmpi(in, 'Params')
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−    varargout{1} = getDefaultPL();
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−    return
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−  elseif strcmpi(in, 'Version')
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−    varargout{1} = VERSION;
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−    return
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−  elseif strcmpi(in, 'Category')
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−    varargout{1} = CATEGORY;
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−    return
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−  end
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−end
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−
+
−%% Collect input ao's, plist's and ao variable names
+
−
+
−in_names = {};
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−
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−for ii = 1:nargin
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−    in_names{end+1} = inputname(ii); % Collect the inputs names
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−end
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−
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−[as, pl, invars] = collect_inputs(varargin, in_names);
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−
+
−% produce one parameter list
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−if isa(pl, 'plist')
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−  pl = combine(pl, getDefaultPL());
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−else
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−  pl = getDefaultPL();
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−end
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−
+
−%% Initialize outputs
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−bs = [];
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−
+
−%% Go through analysis objects
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−
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−% Assigning coefficients values based on the input options
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−switch find(pl, 'ORDER')
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−    case 'FIRST'
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−        Coeffs = [1 -8 0 8 -1]./12;
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−    case 'SECOND'
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−        Coeffs = [-1 16 -30 16 -1]./12;
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−    case 'THIRD'
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−        Coeffs = [-1 2 0 -2 1]./2;
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−    case 'FOURTH'
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−        Coeffs = [1 -4 6 -4 1];     
+
−end
+
−
+
−for jj = 1:numel(as)
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−    
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−    a = as(jj);
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−    phi = a.data.y;
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−    fs = get(a, 'fs');
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−    T = 1/fs;
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−    
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−    %% Building vectors for calculation
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−    phi_temp = [phi(1);phi(1);phi(1);phi(1);phi;phi(end);phi(end);phi(end);phi(end)];
+
−
+
−    % Switching between the input options
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−    switch find(pl, 'ORDER')
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−        case 'FIRST'
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−            Deriv = (1/T).*(Coeffs(1)*phi_temp(1:end-4) + Coeffs(2)*phi_temp(2:end-3) + Coeffs(3)*phi_temp(3:end-2) + Coeffs(4)*phi_temp(4:end-1) + Coeffs(5)*phi_temp(5:end));
+
−            Deriv = Deriv(3:end-2);
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−        case 'SECOND'
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−            Deriv = (1/T^2).*(Coeffs(1)*phi_temp(1:end-4) + Coeffs(2)*phi_temp(2:end-3) + Coeffs(3)*phi_temp(3:end-2) + Coeffs(4)*phi_temp(4:end-1) + Coeffs(5)*phi_temp(5:end));
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−            Deriv = Deriv(3:end-2);
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−        case 'THIRD'
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−            Deriv = (1/T^3).*(Coeffs(1)*phi_temp(1:end-4) + Coeffs(2)*phi_temp(2:end-3) + Coeffs(3)*phi_temp(3:end-2) + Coeffs(4)*phi_temp(4:end-1) + Coeffs(5)*phi_temp(5:end));
+
−            Deriv = Deriv(3:end-2);
+
−        case 'FOURTH'
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−            Deriv = (1/T^4).*(Coeffs(1)*phi_temp(1:end-4) + Coeffs(2)*phi_temp(2:end-3) + Coeffs(3)*phi_temp(3:end-2) + Coeffs(4)*phi_temp(4:end-1) + Coeffs(5)*phi_temp(5:end));
+
−            Deriv = Deriv(3:end-2);
+
−    end
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−    
+
−    %% Building output Aos
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−    
+
−    % Creating new time series data
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−    Deriv = tsdata(Deriv,fs);
+
−
+
−    Deriv = set(Deriv, 'name', ...
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−    sprintf('ltpda_parfit_derivative(%s)', a.data.name), ...
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−    'xunits', a.data.xunits, 'yunits', 'm/s^2');
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−
+
−    % make new history objects
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−    h = history(ALGONAME, VERSION, pl, a.hist);
+
−    h = set(h, 'invars', invars);
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−
+
−    % make output analysis objects
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−    b = ao(Deriv, h);
+
−    clear Deriv
+
−
+
−    % name, mfilename, description for these objects
+
−    b = setnh(b, 'name', sprintf('ltpda_parfit_derivative(%s)', invars{jj}),...
+
−       'description', find(pl,'description'));
+
−
+
−    %% Output the data
+
−
+
−    bs = [bs b];
+
−    clear a b
+
−
+
−end
+
−
+
−%% Reshape the ouput to the same size of the input
+
−varargout{1} = reshape(bs, size(as));
+
−
+
−%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
−%
+
−% FUNCTION:    getDefaultPL
+
−%
+
−% DESCRIPTION: Get default params
+
−%
+
−% HISTORY:     01-02-2008 M Hueller
+
−%                 Creation
+
−%
+
−%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
−function plo = getDefaultPL()
+
−
+
−plo = plist('NAME', 'ltpda_parfit_derivative', 'ORDER', 'SECOND', ...
+
−    'DESCRIPTION','Series Expansion Derivative Method');
+
−
+
−
+
−% END
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−
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−
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−
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−