Survey of various Z-domain to S-domain transformations

The basic objective of this paper is to study the unity in diversity of the various z-domaia to s-domain transformations and find under what conditions they yield similar results. The various transformations include impulse invariant, step invariant, bilinear transformation, ramp invariant transformations, and so on. The second objective is to find out under what conditions the continuous differential equation describing the system may be approximated by a difference equation for all the various z-domaia transformations. The third objective is to find out 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.