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An Error Bound for a Numerical Filtering Technique

An Error Bound for a Numerical Filtering Technique A.n Error Bound for a Numerical Filtering Technique* EDWARD B . ANDERS Northeast Louisiana State College, Monroe, Louisiana Abstract. Let the transfer function for the numerical filter be H(w) = ~ _ _ , h,,e(~'~,~5 where h,~ is the n t h weight and f,~ is the sampling frequency. T h e weights are giwm by h,~ = 1/2rrf,~f'~/;Ti, H(w)e(-*"./f~ ) dw. If we assume t h a t H(w) has a continuous first derivatiw; a~d the second derivative exists, an error bound is given by e(N, f,) =< 2fffrrNf~tc I H'(w) I &.~, where w~ is the angular cut-off frequency, wt the t e r m i n a t i o n frequency, and 2N q- 1 is the n u m b e r of weights used. This is a bound for the error in recovering the transfer fmmtion by using a finite number of weights. Introduction In 1961, Joseph Ormsby [1] proposed ~ numerical filter whose transfer hmetion had the following form: H(w) = w); -w~<w < -w,,, w~ < w < w~ ~1; l'wl ~ w. where w, - cutoff frequency (angulm') = 2,vj'~ and w, = filter roll-off termina*,ion frequency. In general, http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of the ACM (JACM) Association for Computing Machinery

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