Accurate estimation of minimum filter length for optimum FIR digital filters

This paper presents an accurate estimation formula of minimum filter length for optimum (minimax criterion based) linear-phase finite impulse response (FIR) low-pass digital filters. Two estimation formulae have been already proposed; however, they have some problems which lead to wrong estimation. Discussing the problems based on our experimental results, a new estimation formula is newly proposed. The accuracy of the proposed formula is evaluated in comparison with that of the conventional formulae. Furthermore, the proposed formula is applied to the design of high-pass, band-pass, and band-stop filters. The estimation accuracy is discussed also in this case.