On the design of the optimum numerical filter with a prefixed response

Abstract

The number of the coefficients of a numerical filter of
an equispaced time series, corresponding to a given response is generally
unlimited; this number should be limited for obvious computing reasons and
not be greater than a certain value so that two data of the filtered series do
not become dependent from each other, because of the filter.
In this work it is shown how to calculate a filter with a given number
of coefficients whose response is the best approximation to a given response
and meanwhile satisfies to certain desired properties