On the Normalized Slope Descriptor Method of Quantifying Electroencephalograms

Two "exact" sets of normalized slope descriptors, activity, mobility, and complexity, defined in the time domain, are introduced, and their connection with the Hjorth descriptors is discussed. For the set of descriptors obtained by taking the time average on [0, T], where T tends to infinity, the corresponding expressions in the frequency domain are also given, together with their relationships with the expected number of zeros and extrema of the signal. The relationships connecting the three mathematically distinct sets of descriptors are illustrated numerically using signals of the form ƒ(t) =Σ
^N
_i=1
u
_i
sin 2πv
_i
t, which are also used to emphasize that Hjorth's complexity may not necessarily exist.