Closed-form design of sharp FIR half-band filters, Hilbert transformer, and differentiator

A novel design of linear-phase sharp FIR filters is presented in a closed form by employing sampling kernels and relationships among half-band filters, Hilbert transformers, and differentiators. Design examples demonstrate that three designed sharp FIR filters (i.e., half-band filter, Hilbert transformer, and differentiator) can be easily and directly obtained with small number of multipliers and reduced group delay.