Accuracy and stability of discrete-time filters generated by higher-order s-to-z mapping functions

This note compares several different approaches to selecting an s-to-z mapping function for the purpose of converting a continuous-time transfer function F(s) to an “equivalent” discrete-time transfer function F_D(z). The primary bases of comparison are stability and accuracy. Secondary bases of comparison include: 1) the amount of computation needed to process one input to produce one output, 2) the ease with which the coefficients of F_D(z) can be determined, in particular, as the sampling period T is varied, 3) the ease of determining stability, in particular, the maximum value of T for stability, 4) the self-starting capability, and 5) compatibility with decomposition in the s-domain