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Although a great deal is known about design techniques for optimum (in a minimax error sense) finite impulse response (FIR) low‐pass digital filters, there have not been established any practical design rules for such filters. Thus, a user is unable to easily decide on the (approximate or exact) filter order required to meet his design specifications and must resort to tables or trial and error procedures. In this paper, such a set of design rules is given. In the case of very narrow bandwidth or very wide bandwidth filters, analytic relations between the filter parameters can be readily obtained. In all other cases, exceedingly good linear and nonlinear fits to the data can be obtained over somewhat restricted ranges of the parameters. These fitting procedures lead to a practical set of simple design rules for estimating filter order from the desired specifications.

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The purpose of this paper is to make comparisons between optimum, linear phase, finite impulse response (FIR) digital filters and infinite impulse response (IIR) digital filters which meet equivalent frequency domain specifications. The basis of comparison is, for the most part, the number of multiplications per sample required in the usual realizations of these filters–‐i.e., the cascade form for IIR filters, and the direct form for FIR filters. Comparisons are also made between group‐delay equalized filters and linear phase FIR filters. Considerations dealing with finite word‐length effects are discussed for both these filter types. A set of design charts is also presented for determining the minimum filter order required to meet given low‐pass filter specifications for both digital and analog filters.