### On Exponential Digital FiltersOn Exponential Digital Filters

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 Author Blum, Marvin Source ACM Digital Library Content type Text Publisher Association for Computing Machinery (ACM) File Format PDF Copyright Year ©1959 Language English
 Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science Abstract This paper derives the weighting sequence of a linear digital filter whose output is an estimate of the predicted values of the derivatives of the input. The input functions considered are arbitrary linear combinations of $\textit{n}$ + 1 known functions, plus a random stationary signal and a random stationary noise component. The filter differs from previously considered minimum variance optimum filters in that the primary consideration here is the computational ease with which one can obtain the final solution. An optimization in the minimum variance sense is obtained as a secondary consideration in order to provide some control of the mean square output error. The exponential filter has its simplest form for the class of nonrandom input functions $(\textit{hn})$ which are the complete solutions of a set of homogeneous linear difference equations of order $\textit{n}$ with constant coefficients. For this class the input and output are related by a time invariant recursion formula. The output contains a bias error which can be made to approach zero exponentially as the mean square error increases monotonically to a limit with increasing time.A modification of the exponential filter is considered such that the bias error is zero. The solution then involves a recursion formula with time varying coefficients. ISSN 00045411 Age Range 18 to 22 years ♦ above 22 year Educational Use Research Education Level UG and PG Learning Resource Type Article Publisher Date 1959-04-01 Publisher Place New York e-ISSN 1557735X Journal Journal of the ACM (JACM) Volume Number 6 Issue Number 2 Page Count 22 Starting Page 283 Ending Page 304

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Source: ACM Digital Library