An Analytical Method for the Multiplierless 2-D FIR Filter Functions and Hilbert Transform in $z2$ Domain

A novel analytical method for the new class of linear-phase multiplierless 2-D finite-impulse response (FIR) digital filter functions generated by applying the Christoffel-Darboux formula for classical Chebyshev polynomials of the first and the second kind, in a compact explicit representative form, is proposed in this brief. Correct transformation from a continuous 2-D domain into the z domains without residuum and without errors is described. The proposed solution with high selectivity is a filter function in the z1 domain and the Hilbert transformer in the z2 domain. A corresponding example of the new class of linear-phase highly selective 2-D FIR digital filters of low complexity, which is obtained by the proposed approximation technique, is shown in this brief.