+
−function   varargout = ltpda_free_dynamics(varargin)
+
−%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
−%
+
−% DESCRIPTION: DATA_REDUCTION converts interferometer data to acceleration
+
−% data. This function returns the free dynamics without the action of the
+
−% controller circuit. The commanded force has to be subtracted in order to
+
−% obtain the output force noise
+
−%
+
−%
+
−% CALL:                 b = ltpda_free_dynamics(varargin);
+
−%                       ltpda_free_dynamics(varargin);
+
−%
+
−% INPUTS:      
+
−%       - Aos containing the interferometer data. Aos must be supplied in
+
−%       couples.
+
−%       - plist containing the parasitic stiffness and the cross talk
+
−%       coefficient. The default structure of the plist is:
+
−%           plo = plist('pstiff1', -13e-7,'pstiff2', -20e-7,'cross_talk',
+
−%           -1e-4, 'METHOD', 'PARFIT')
+
−%           - 'pstiff1' is the square of the parasitic stiffness per unit of mass of TM1
+
−%           - 'pstiff2' is the square of the parasitic stiffness per unit of mass of TM2
+
−%           - 'cross_talk' is the sensitivity of the differential channel
+
−%           to x1
+
−%           - 'METHOD' define the method you want to use for the
+
−%           calculation of the derivatives. Possible values are:
+
−%               - 'PARFIT' makes use of the five points stencil parabolic
+
−%               fit approximation [1] to calculate the derivatives
+
−%               - 'SERIES' makes use of the five points stencil taylor
+
−%               series approximation [2] to calculate the derivatives
+
−% 
+
−%       Es: b = ltpda_free_dynamics(ao1, ao2);
+
−% 
+
−%       Es: b = ltpda_free_dynamics(ao1, ao2, pl);
+
−%              
+
−%
+
−%
+
−% OUTPUTS:     
+
−%       a vector of Aos containing the data obtained by the application of
+
−%       the free dynamics to the input data (interferometer data)
+
−%
+
−% REFERENCES:
+
−%           [1] L. Carbone et al., Physical Review D 75, 042001 (2007)
+
−%           [2] S. E. Koonin and D. C. Meredith, COMPUTATIONAL PHYSICS -
+
−%           Fortran Version, 1990, Westview Press
+
−%
+
−% VERSION:     $Id: ltpda_free_dynamics.m,v 1.1 2008/04/24 16:13:12 luigi Exp $
+
−% 
+
−% HISTORY:     18-03-2008 L Ferraioli
+
−%                 Creation
+
−%
+
−%
+
−%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
−
+
−
+
−
+
−%% Standard history variables
+
−
+
−ALGONAME = mfilename;
+
−VERSION  = '$Id: ltpda_free_dynamics.m,v 1.1 2008/04/24 16:13:12 luigi Exp $';
+
−CATEGORY = 'Signal Processing';
+
−
+
−%% Check if this is a call for parameters, the CVS version string
+
−% or the method category
+
−if nargin == 1 && ischar(varargin{1})
+
−  in = char(varargin{1});
+
−  if strcmpi(in, 'Params')
+
−    varargout{1} = getDefaultPL();
+
−    return
+
−  elseif strcmpi(in, 'Version')
+
−    varargout{1} = VERSION;
+
−    return
+
−  elseif strcmpi(in, 'Category')
+
−    varargout{1} = CATEGORY;
+
−    return
+
−  end
+
−end
+
−
+
−%% Collect input ao's, plist's and ao variable names
+
−in_names = {};
+
−for ii = 1:nargin
+
−  in_names{end+1} = inputname(ii);
+
−end
+
−
+
−[as, pl, invars] = collect_inputs(varargin, in_names);
+
−
+
−% Checks that the input AOs come in pairs
+
−if rem(length(as),2)
+
−  warning('The input AOs must come in pairs!');
+
−  return
+
−end
+
−
+
−% produce one parameter list
+
−if isa(pl, 'plist')
+
−  pl = combine(pl, getDefaultPL());
+
−else
+
−  pl = getDefaultPL();
+
−end
+
−
+
−%% Initialize outputs
+
−% bs = [];
+
−
+
−%% Defining Constants
+
−
+
−fs = get(as(1),'fs');
+
−wpx1 = find(pl, 'pstiff1');
+
−wpx2 = find(pl, 'pstiff2');
+
−dSD1 = find(pl, 'cross_talk');
+
−T = 1/fs;
+
−
+
−%% Defining plist for derivative functions
+
−
+
−% In this case we need only second order derivatives and zero order in
+
−% case we want to use the parabolic fit method
+
−pl_2diff = plist('NAME', 'Second deriv plist', 'ORDER', 'SECOND');
+
−pl_0diff = plist('NAME', 'Zero deriv plist', 'ORDER', 'ZERO');
+
−
+
−%% Going through analysis objects
+
−
+
−for jj = 1:2:numel(as)/2
+
−          
+
−    % Extracts the input data
+
−    a1 = as(jj);
+
−    a2 = as(jj+1);
+
−    
+
−    %% Applying "free dynamics" to data using the differentiation method
+
−    %% defined in the input plist
+
−    switch find(pl, 'METHOD')
+
−        case 'PARFIT'
+
−            d2_a1 = ltpda_parfit_derivative(a1, pl_2diff);
+
−            d0_a1 = ltpda_parfit_derivative(a1, pl_0diff);
+
−            d2_a2 = ltpda_parfit_derivative(a2, pl_2diff);
+
−            d0_a2 = ltpda_parfit_derivative(a2, pl_0diff);
+
−            
+
−            b1 = d2_a1 + wpx1.*d0_a1;
+
−            b12 = -dSD1.*d2_a1 + (wpx2-wpx1-(dSD1*wpx2)).*d0_a1;
+
−            b22 = d2_a2 + wpx2.*d0_a2;
+
−            b2 = b12 + b22;
+
−            clear b12 b22
+
−            
+
−        case 'SERIES'
+
−            d2_a1 = ltpda_series_derivative(a1, pl_2diff);
+
−            d2_a2 = ltpda_series_derivative(a2, pl_2diff);
+
−            
+
−            b1 = d2_a1 + wpx1.*a1;
+
−            b12 = -dSD1.*d2_a1 + (wpx2-wpx1-(dSD1*wpx2)).*a1;
+
−            b22 = d2_a2 + wpx2.*a2;
+
−            b2 = b12 + b22;
+
−            clear b12 b22
+
−    end
+
−
+
−    % name, mfilename, description for these objects
+
−    b1 = setnh(b1, 'name', sprintf('ltpda_free_dynamics(%s)', invars{jj}),...
+
−       'description', find(pl,'description'));
+
−    b2 = setnh(b2, 'name', sprintf('ltpda_free_dynamics(%s)', invars{jj+1}),...
+
−        'description', find(pl,'description'));
+
−%     bs = [bs b1 b2];
+
−%     clear('b1', 'b2');
+
−    
+
−end
+
−
+
−% %% Reshape the ouput to the same size of the input
+
−% 
+
−% varargout{1} = reshape(bs, size(as));
+
−
+
−%% outputs
+
−if nargout == 2
+
−   varargout{1} = b1;
+
−   varargout{2} = b2;
+
−elseif nargout == 1
+
−   varargout{1} = [b1 b2];
+
−end
+
−%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
−%
+
−% FUNCTION:    getDefaultPL
+
−%
+
−% DESCRIPTION: Get default params
+
−%
+
−% HISTORY:     01-02-2008 M Hueller
+
−%                 Creation
+
−%
+
−%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
−function plo = getDefaultPL()
+
−
+
−plo = plist('pstiff1', -13e-7,'pstiff2', -20e-7,'cross_talk', -1e-4,'METHOD', 'PARFIT', ... 
+
−    'DESCRIPTION','Application of the free dynamics to interferometer data');
+
−
+
−
+
−
+
−
+
−
+
−
+
−
+
−