Some Transforms for Modelling of Computing Anticipatory Systems

In this paper, we introduce and investigate transforms mapping the space of continuous signals into the space of discrete signals. These transforms map the derivative of an arbitrary order into the forward, the backward, and the average difference. The introduced transforms permit to derive discrete modells for continuous time systems described by differential equations. Since a transform mapping the derivatives into the average differences is provided, modeling of continuous time systems by computing anticipatory systems is included. Application of introduced transforms is illustrated by deriving the discrete modells for harmonic oscillators.