function [FuzzyEn] = FuzzyEn(series,dim,r,n)
%{
Function which computes the Fuzzy Entropy (FuzzyEn) of a time series. The
alogorithm presented by Chen et al. at "Charactirization of surface EMG
signal based on fuzzy entropy" (DOI: 10.1109/TNSRE.2007.897025) has been
followed.
INPUT:
series: the time series.
dim: the embedding dimesion employed in the SampEn algorithm.
r: the width of the fuzzy exponential function.
n: the step of the fuzzy exponential function.
OUTPUT:
FuzzyEn: the FuzzyEn value.
PROJECT: Research Master in signal theory and bioengineering - University of Valladolid
DATE: 11/10/2014
VERSION: 1�
AUTHOR: Jes�s Monge �lvarez
%}
%% Checking the ipunt parameters:
control = ~isempty(series);
assert(control,'The user must introduce a time series (first inpunt).');
control = ~isempty(dim);
assert(control,'The user must introduce a embbeding dimension (second inpunt).');
control = ~isempty(r);
assert(control,'The user must introduce a width for the fuzzy exponential function: r (third inpunt).');
control = ~isempty(n);
assert(control,'The user must introduce a step for the fuzzy exponential function: n (fourth inpunt).');
%% Processing:
% Normalization of the input time series:
series = (series-mean(series))/std(series);
N = length(series);
phi = zeros(1,2);
% Value of 'r' in case of not normalized time series:
% r = r*std(series);
for j = 1:2
m = dim+j-1; % 'm' is the embbeding dimension used each iteration
% Pre-definition of the varialbes for computational efficiency:
patterns = zeros(m,N-m+1);
aux = zeros(1,N-m+1);
% First, we compose the patterns
% The columns of the matrix 'patterns' will be the (N-m+1) patterns of 'm' length:
if m == 1 % If the embedding dimension is 1, each sample is a pattern
patterns = series;
else % Otherwise, we build the patterns of length 'm':
for i = 1:m
patterns(i,:) = series(i:N-m+i);
end
end
% We substract the baseline of each pattern to itself:
for i = 1:N-m+1
patterns(:,i) = patterns(:,i) - (mean(patterns(:,i)));
end
% This loop goes over the columns of matrix 'patterns':
for i = 1:N-m
% Second, we compute the maximum absolut distance between the
% scalar components of the current pattern and the rest:
if m == 1
dist = abs(patterns - repmat(patterns(:,i),1,N-m+1));
else
dist = max(abs(patterns - repmat(patterns(:,i),1,N-m+1)));
end
% Third, we get the degree of similarity:
simi = exp(((-1)*((dist).^n))/r);
% We average all the degrees of similarity for the current pattern:
aux(i) = (sum(simi)-1)/(N-m-1); % We substract 1 to the sum to avoid the self-comparison
end
% Finally, we get the 'phy' parameter as the as the mean of the first
% 'N-m' averaged drgees of similarity:
phi(j) = sum(aux)/(N-m);
end
FuzzyEn = log(phi(1)) - log(phi(2));
end %End of the 'FuzzyEn' function
