savgol (x, wi, or, deriv)

%Function savgol
%
%This function performs savitsky-golay preprocessing on a spectrum.
%
%Syntax:
%    SG = savgol (x, wi, or, deriv)
%
%Parameters:
%    x: the dataset, one row is one spectrum
%    wi: width of the window
%    or: order of the polynomial
%    deriv: order of the derivative of the polynomial
%    SG: the preprocessed dataset
%
%Example:
%    load data
%    xaxis = 1:size(data,1);
%    subplot (2,1,1);
%    plot (xaxis, data);
%    title ('Original dataset');
%    subplot (2, 1, 2);
%    plot (xaxis, savgol (data, 13, 2, 1));
%    title ('First derivative');

%This software package is dual licensed. You can use it according to the terms
%of either the GPLv3 or the BSD license.
%
%C 2007, Kris De Gussem, Raman Spectroscopy Research Group, Department
%of analytical chemistry, Ghent University
%
%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
%(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.
%
%You should have received a copy of the GNU General Public License
%along with this program.  If not, see
%http://www.gnu.org/licenses/.

%Copyright (c) 2007, Kris De Gussem
%All rights reserved.
%
%Redistribution and use in source and binary forms, with or without 
%modification, are permitted provided that the following conditions are 
%met:
%
%    * Redistributions of source code must retain the above copyright 
%      notice, this list of conditions and the following disclaimer.
%    * Redistributions in binary form must reproduce the above copyright 
%      notice, this list of conditions and the following disclaimer in 
%      the documentation and/or other materials provided with the distribution
%    * Neither the name of Raman Spectroscopy Research Group, Department of
%	  analytical chemistry, Ghent University nor the names 
%      of its contributors may be used to endorse or promote products derived 
%      from this software without specific prior written permission.
%      
%THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" 
%AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 
%IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 
%ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE 
%LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR 
%CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF 
%SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS 
%INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN 
%CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) 
%ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE 
%POSSIBILITY OF SUCH DAMAGE.

function SG = savgol (x, wi, or, deriv)
g = sgsdf(-(wi-1)/2:(wi-1)/2, or, deriv);   % Calculate S-G coefficients
[n,m] = size(x);
g=repmat(g,n,1);

HalfWin  = ((wi+1)/2) -1;
EOS = m-(wi+1)/2+1;
SG = zeros(n,m);
for i = (wi+1)/2:EOS
    SG(:,i) = dot(g, x(:,i - HalfWin: i + HalfWin),2);
end

cb = EOS+1:m;
SG(:,cb) = repmat (SG(:,EOS), 1, length (cb));