Permutation entropy of EEG signals for different sampling rate and time lag combinations

Permutation entropy (PE) measure is investigated for the cases when different time lags are used to obtain embedded vectors and the signal under analysis has different sampling rate. PE of orders from 2 to 5 was calculated for the electroencephalogram signals from healthy patients for raw signal and sequence of downsampled signals with different time lags. For various combinations of downsampling factor and time lag the averaged PE plots indicated that PE of a signal appears to be the same for certain combinations. It is defined that PE values would be equal for combinations of integer lags and downsampling factors whose product gives same result. The need of specifying both time lag and sampling rate or time interval between samples in patterns, when studying permutation entropy is emphasized, and this can be extended to other techniques employing the embedded patterns analysis.