SURVEY OF VARIOUS Z-DOMAIN TO S-DOMAIN TRANSFORMATIONS.

The unity in diversity of the various z-domain to s-domain transformations are analyzed, and the conditions under which they yield similar results are determined. It is shown that the various z-domain to s-domain transformations are pole invariant transformations, (they all yield the same poles for the system, however the zeros are different). It is determined under what conditions the continuous differential equation describing the system may be approximated by a difference equation for all the various z-s domain transformations. It is then determined under what assumptions the discrete version of the impulse response becomes a sampled version of the continuous response. Finally, numerical results are presented to study the degree of accuracy of various approximations as a function of the sampling rate.