Mathematical proof of explicit formulas for tap-coefficients of full-band FIR digital differentiators

Explicit formulas for the tap-coefficients of Taylor-series-based full-band FIR digital differentiators have already been presented. However, those formulas were not derived mathematically from the Taylor series and were based on observations of different sets of results. The authors provide a mathematical proof of the formulas by deriving them mathematically from the Taylor series