Event Detection: Qrs-Complexes in Ecg Signals - microLab

BioMedSigProcAnawhereas the form (1b) could be implemented in direct form asy[n] = y[n − 1] + 1 Nor, in what is called the canonical form, as()x[n] − x[n − N] , (3)w[n] = w[n − 1] + x[n]y[n] = 1 ()w[n] − w[n − N] ;N(4)here in (4) w[n] is a newly introduced interval variable—an internalsignal—of the filter.Comparing the feed-forward implementation (2) to the recursiveimplementations either (3) or (4), we see that the numberof operations needed to compute one output sample favorsthe recursive implementations. This lower computational effortis the reason that many books on biomedical signal processingsuggest the recursive implementations.We note, however, that the recursive implementations mightbecome problems with error accumulation and instability—theimplementations (3) and (4) both have a pole at z = 1, whichis not strictly inside of the unit circle. To get a feeling of whatmight happen, consider the canonical implementation (4) andassume that the input signal is a white-noise signal. 4 The equationw[n] = w[n − 1] + x[n] is an accumulator, and accumulatinga white-noise sequence gives a non-stationary stochasticprocess with a linearly increasing variance, meaning that w[n]must sooner or later become unstable, which is, of course, notacceptable. Similar considerations for the implementation (3)lead to the same conclusions. We do not go into more details,but, instead, refer to [Orf96], where these issues are discussedon pages 402 ff., and which has an Appendix A, pages 728 ff.,discussing discrete-time random signals and their filtering.4 A discrete-time white noise signal is a sequence where any two samplesare uncorrelated.6 EventDet 19 2014