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

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