An order estimator for magnitude constrained FIR Nyquist filters

Order estimation is an often task of filter design. For a general-purpose finite impulse response (FIR) filter, the formulas relating the filter order, the magnitude error bounds and the transition widths are well known. These formulas, however, are not appropriate for Nyquist FIR filters. This paper presents a formula that estimates the minimum order of a Nyquist filter with prescribed magnitude error bounds. Simulation examples and comparisons with existing methods demonstrate that the presented formula has very high accuracy.