Higher Order s-to-z Mapping Functions for Digital Filters

Digital filters are frequently designed by taking an analog (continuous-time) filter and converting it into its digital (discrete-time) equivalent. Linear, time-invariant discrete¬time filters with fixed sampling rates are usually designed by conversions from the analog using bilinear transformation. This book deals with conversions from analog domain into digital domain by higher order s-to-z transformations. By using higher order rules, we obtain better accuracy in digitizing continuous-time filters. Unlike the bilinear transformation, the higher order rules do not have a stability region which cover the entire left-half of the s-plane. The sampling period used in the digitizing process has to be selected in such a way that all the poles of the continuous-time filter lie inside the stability region of the selected rule. Otherwise, the discrete-time filter will be unstable. The start-up error obtained due to the discontinuity in the input signal is also discussed.