Unified Filter Order Estimate for Minimax-Designed Linear-Phase FIR Wideband and Lowpass Digital Differentiators

Digital differentiators enable the computation of the derivative of a continuous-time signal at discrete time instances, and they are used in many signal processing applications. This paper derives a unified filter order estimate for digital differentiators that are realized with linear-phase finite-length impulse response filters and designed in the minimax sense. The estimate is useful at the high-level system design when assessing the implementation complexity and it enables fewer designs when finding the minimal filter order required to satisfy a prescribed tolerable approximation error. The proposed unified estimate covers both wideband and lowpass differentiators of integer degrees up to ten. Furthermore, degree-individual filter order estimates are derived which improve and extend previous results. The performance of both the unified and degree-individual order estimates is evaluated through simulation examples and compared with previous estimates.