Practical Design Rules for Optimum Finite Impulse Response Low-Pass Digital Filters

Abstract

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.

Estimation of filter order for prescribed, reduced group delay FIR filter design

“…They can also be implemented for bandpass and bandstop filters, assuming for calculation the width of the narrower transition band. The formulas yield better precision for FIR filters with an odd number of coefficients, as they were derived for such filters [8]. Moreover, the precision of filter order estimation decreases for filters with a very large number of coefficients.…”

“…For linear-phase FIR filters and an equiripple magnitude response, the formula (derived in an experimental manner) was proposed by Hermann, Rabiner and Chan [8,9]:…”

“…[17][18][19][20]. The value obtained from (2) is smaller by one when compared with source formulas given in [8] and [9], because M in this paper denotes the filter order, whereas in [8] and [9] it denotes the number of coefficients (filter length). The formulas can be applied for wide ranges of passband edges ω p for lowpass and highpass filters.…”

“…One of the problems that appear while applying the given methods is calculation of the filter order. Formulas for filter order calculation presented in the literature [8][9][10][11] have been elaborated for linear-phase FIR filters. In the given paper, the formula for filter order calculation based on a prescribed group delay in the passband as well as other filter parameters (the width of the transition band and magnitude response approximation error in the passband and stopband) has been derived.…”

Precise interpolation for band‐limited digital signals based on sampling theorem incorporated with window functions

“…Here, the following is known as the empirical equation to evaluate the impulse response length of the equal ripple filter [7]: where c 1 , c 2 , and c 3 are constants, N f g is the half-width of the impulse response h eqr n of the filter, G 1 and G 2 are the parameters to indicate the ripples in the passband and the stopband defined above, and 'Z is the transition bandwidth normalized by the sampling angular frequency. [For G 1 , G 2 , and 'Z, see Figs.…”