Characterization of Surface EMG Signal Based on Fuzzy Entropy

Fuzzy entropy (FuzzyEn), a new measure of time series regularity, was proposed and applied to the characterization of surface electromyography (EMG) signals. Similar to the two existing related measures ApEn and SampEn, FuzzyEn is the negative natural logarithm of the conditional probability that two vectors similar for $m$ points remain similar for the next $m +1$ points. Importing the concept of fuzzy sets, vectors' similarity is fuzzily defined in FuzzyEn on the basis of exponential function and their shapes. Besides possessing the good properties of SampEn superior to ApEn, FuzzyEn also succeeds in giving the entropy definition in the case of small parameters. Its performance on characterizing surface EMG signals, as well as independent, identically distributed (i.i.d.) random numbers and periodical sinusoidal signals, shows that FuzzyEn can more efficiently measure the regularity of time series. The method introduced here can also be applied to other noisy physiological signals with relatively short datasets.