Abstract
Abstract The principal advantage of using higher-order mapping functions is increased accuracy in digitizing linear, time-invariant, continous-time filters for real-time applications. 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. 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. Performance improvement of digital filters derived from higher-order s-to-z mapping functions, as compared to those derived from linear mapping functions, is demonstrated through the use of examples. Analysis to demonstrate improvement is carried out in both the time and frequency domains.
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