SampleEntropy.rar_matlab_sampleEntropy_信号 熵_样本熵_样本熵的参数

function SampEn = SampleEntropy(x,m,r,sflag) % SampEn = SampleEntropy(x,m,r,sflag) % % Obligatory inputs: % x - input signal vector (e.g., EEG signal or sound signal) % % Optional inputs (defaults): % m = 2; % template length (epoch length) % r = 0.2; % matching threshold (default r=.2), when standardized: defined the tolerance as r times the standard deviation % sflag = 1; % 1 - standardize signal (zero mean, std of one), 0 - no standarization % % Output: % SampEn - sample entropy estimate (for a sine tone of 1s (Fs=44100) and r=0.2, m=2, the program needed 3.3min) % % References: % Richman JS, Moorman, JR (2000) Physiological time series analysis using approximate % entropy and sample entropy. Am J Physiol 278:H2039-H2049 % Abasolo D, Hornero R, Espino P, Alvarez D, Poza J (2006) Entropy analysis of the EEG % background activity in Alzheimer’s disease patients. Physioogical Measurement 27:241–253. % Molina-Pico A, Cuesta-Frau D, Aboy M, Crespo C, Miró-Martínez P, Oltra-Crespo S (2011) Comparative % study of approximate entropy and sample entropy robustness to spikes. Artificial Intelligence % in Medicine 53:97–106. % % The first reference introduces the method and provides all formulas. But see also these two references, % because they depict the formulas much clearer. If you need a standard error estimate have a look at (or the papers): % http://www.physionet.org/physiotools/sampen/ % % Description: The program calculates the sample entropy (SampEn) of a given signal. SampEn is the negative % logarithm of the conditional probability that two sequences similar for m points remain similar at the next % point, where self-matches are not included in calculating the probability. Thus, a lower value of SampEn % also indicates more self-similarity in the time series. % % --------- % % Copyright (C) 2012, B. Herrmann % 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/>. % % ----------------------------------------------------------------------------------------------------- % B. Herrmann, Email: [email protected], 2012-01-15 % check inputs SampEn = []; if nargin < 1 || isempty(x), fprintf('Error: x needs to be defined!\n'), return; end if ~isvector(x), fprintf('Error: x needs to be a vector!\n'), return; end if nargin < 2 || isempty(m), m = 2; end if nargin < 3 || isempty(r), r = 0.2; end if nargin < 4 || isempty(sflag), sflag = 1; end % force x to be column vector x = x(:); N = length(x); % normalize/standardize x vector if sflag > 0, x = (x - mean(x)) / std(x); end % obtain subsequences of the signal Xam = zeros(N-m,m+1); Xbm = zeros(N-m,m); for ii = 1 : N-m % although for N-m+1 subsequences could be extracted for m, Xam(ii,:) = x(ii:ii+m); % in the Richman approach only N-m are considered as this gives the same length for m and m+1 Xbm(ii,:) = x(ii:ii+m-1); end % obtain number of matches B = zeros(1,N-m); A = zeros(1,N-m); for ii = 1 : N-m % number of matches for m d = abs(bsxfun(@minus,Xbm((1:N-m)~=ii,:),Xbm(ii,:))); B(ii) = sum(max(d,[],2) <= r); % number of matches for m+1 d = abs(bsxfun(@minus,Xam((1:N-m)~=ii,:),Xam(ii,:))); A(ii) = sum(max(d,[],2) <= r); end % get probablities for two sequences to match B = 1/(N-m-1) * B; % mean number of matches for each subsequence for m Bm = 1/(N-m) * sum(B); % probability that two sequences will match for m points (mean of matches across subsequences) A = 1/(N-m-1) * A; % mean number of matches for each subsequence for m+1 Am = 1/(N-m) * sum(A); % probability that two sequences will match for m+1 points (mean of matches across subsequences) cp = Am/Bm; % conditional probability SampEn = -log(cp); % sample entropy