332 Information Storage and Neural Control 



DERIVATIVE CHARACTERISTICS 



"to 56 66 



TfMSSSKt (CTCIXB m SBXMD) 



Fig. 1. Electronic Parameters of the Mathematical Derivative. The 90° phase shift and 

 linear doubhng of ampHtude per octave is illustrated as the electronic definition 

 of a first derivative. The sharply increasing amplitude of the second derivative 

 with increase in frequency emphasizes the accentuation of high frequency com- 

 ponents. The three functions on the right of the figure graphically illustrate the 

 eff'ect of derivative processing. 



differentiating network to yield the first derivative, / (v) . The first 

 derivative, through an identical differentiating network, gives the 

 first derivative of the first derivative, or second derivative, /"(v), 

 of the primary evoked potential. These functions, after Lorente 

 de No (7), illustrate the external action potential of bullfrog 

 alpha fibers and its first two derivatives. It is clear that the high 

 frequency components of the primary evoked potential are greatly 

 accentuated by double differentiation. The electronic definition 

 of a derivative is the same as the mathematical definition except 

 that it is couched in different parameters. The phase shift required 

 in a sine wave is 90° for the first derivative and 180° for the second 

 derivative. The important parameter for our purpose is the 

 amplitude characteristic as illustrated in Figure 1. Given a mixed 

 sine wave made up of equal amplitude twenty cycle per second 

 and forty cycle per second components, the first derivative will 

 yield twice as much amplitude for the forty cycle per second 

 component because it is twice the frequency of the twenty cycle 



