ADAPTIVE DEGREE SMOOTHING AND DIFFERENTIATION (Scipts) 1.0

% function ynew=adsmoothdiff(dados,xnew,sdx,isdx,q,nmin)% written by Carlos J Dias%% ADAPTIVE DEGREE SAVISTZKY-GOLAY SMOOTHING AND DIFFERENTIATION% This function smooths and differentiates a sequence of numbers based on% an algorithm drawn on the ideas of Savistky and Golay and Barak.% There are no restrictions however, on the number of points% or on their spacing.% This function also calculates the first derivative at the xnew points%% INPUT:% dados - data in a two column matrix (first column x; second column y)% xnew - is a vector where new ordinates are to be computed%% sdx - is the abscissa range of data to be used to find the least squares% polynomial% isdx - is a fraction of the sdx range between [0 1] where new y_values% for xnew will be calculated. It usually is 0.8 (i.e. 80%) of the sdx range.% q - is the highest degree of the polynomial to be used in the interpolation% nmin - is the minimum data points to be used in the interpolation.%% ALGORITHM:% For each point xnew_i of the xnew vector, this function finds the least% squares polynomial (with polyfit) passing through the experimental points% lying between [xnew_i - sdx, xnew_i + sdx].% The degree of the polynomial is chosen based on a F-statistic.% Using this polynomial it calculates, with polyval, the values for% y and its derivative in that same interpolating window.%% All calculated values for each abscissa are used to compute an average% value of the smoothed function and its derivative.% When sdx range includes fewer points than nmin, the range is enlarged to% include at least nmin points. This may occur more often at the edges% of the data.% Note that we should have nmin>q%% OUTPUT (ynew - 5 column matrix)% column 1- new abscissas% column 2- new ordinates% column 3- their standard error% column 4- first derivative% column 5- no. of values that were calculated for the ith point%% DEMO SCRIPT (SMOOTHING OF 1000 POINTS)% x=linspace(-10,10,1000)';% y=1./(1+((x-2)/0.5).^2)+2./(1+((x+2)/0.5).^2);%two lorenztians% noise=0.5*(rand(length(y),1)-0.5);% y=y+noise;% ynew=adsmoothdiff([x y],x,1.1,0.8,11,15);% %(it takes about 30 s to run this script in my computer)%% P Barak, Analytical Chemistry 1995, 67 2758-2762% A Savitzky, MJE Golay, Analytical Chemistry 1964, 36(8) 1627-1638% I also acknowledge Jianwen Luo for drawing my attention to adaptive% strategies.

Requirements:	No special requirements
Platforms:	Matlab
Keyword:	Enlarged,  Fewer,  Include,  Includes,  Nminq,  Occur,  Output,  Smoothed
Users rating:	0/10