Information Processing in the Time Domain 331 



take those," or "No, that's low information, drop that." If we 

 speculate that our demon is extremely conservative and expects 

 the signal to be linear as a function of time, a straight line deter- 

 mined by two or more points, then any point that agrees with this 

 assumption is a low information point. The demon has predicted 

 that the signal will not change from positive to negative values, 

 will not change its sense of positive-negative direction, will not 

 even change its sense of curvature. The high information points 

 now become zero points, minimax points and points of inflection 

 in the primary signal. The coding points generated are at the 

 baseline cross of the primary signal, of its first derivative and of 

 its second derivative. We might have a second type of demon, 

 a neurophysiological demon, that can tell us when a significant 

 neurophysiological event is reflected in the signal. This demon 

 identifies our semantic information as contrasted to statistical 

 information. It would be nice, of course, if both these demons 

 were the same. In order to "twin" our two friends, we would be 

 forced to assume that the brain sees change and rate of change of 

 the electrical potentials in its subpopulations as highly significant in- 

 formation. We would also conclude that the wave shape of our EEG 

 signal is rich in semantic information as compared to characteri- 

 zations in the frequency domain such as frequency or power spectra. 



Defining the coding points for amplitude sampling as the baseline 

 cross of the primary and its first and second deri\^atives allows us 

 to take discrete data in a definite but not uniformly spaced pattern 

 (Case 3). This, on the average, should result in fewer sampling 

 points than the folding, or Nyquist, frequency requirement (5) 

 discussed previously. Period analysis is a further simplification of 

 this general process in that the amplitude of the function is not 

 sampled at all. The theoretical justification for this approach has 

 been developed in terms of the Gram-Charlier series (6). The 

 remainder of this paper will explore period analysis as a special 

 case (Case 4) of information processing in the time domain. The 

 questions to be asked concern retention of both statistical and 

 semantic information during period analysis of several bio- 

 electronic signals. 



Figure 1 illustrates the characteristics of the first and second 

 derivatives. The function /(.v) in the upper right hand corner of 

 the figure represents an evoked potential which feeds into a 



