Ultra‐selective spike multiplierless linear‐phase two‐dimensional FIR filter function with full Hilbert transform effect

Abstract

In this study, a novel analytical method for new class of linear-phase two-dimensional (2D) finite impulse response (FIR) filter functions with full effect of Hilbert transformer in z 1 and z 2 domains generated by applying a new modified 2D Christoffel–Darboux formula for classical orthogonal Chebyshev polynomials of the first and the second kind is proposed. Fundamental research proposed in this study is also illustrated by examples of 2D FIR filter, Hilbert transformer and adequate comparison with new class of multiplierless linear-phase 2D FIR filter function given in the literature. For all 2D FIR filter functions, comparisons are made for the same values of free real parameters, and they show the improvement of the spike sharpness.