Higher order s-to-z mapping functions and their application in digitizing continuous-time filters

A family of higher order numerical integration formulas and their corresponding s-to-z mapping functions are presented. Two of the main problems are stability and handling discontinuous inputs. The stability question is resolved by analyzing the stability regions of the mapping functions relative to the Nyquist sampling criterion. Sources of error in the accuracy of the output of digitized filters relative to their continuous-time counterparts are explored. Techniques for digitizing continuous-time filters, using the mapping functions, are developed for reducing different sources of error, including error resulting from discontinuous inputs