1D linear-phase band-pass multiplierless FIR Hilbert transformers and filters

An original analytical method, based on modified Christoffel–Darboux formula, is used in the paper in order to synthesise a linear-phase band-pass finite impulse response (FIR) filter function that can have an effect of Hilbert transformer. New structure of the band-pass FIR filter in recursive realisation, together with the corresponding difference equation, is presented providing the efficient filter solution without multipliers. Several examples of filter types for different parity of two real free integer parameters, including a particular solution of Hilbert transformer, are considered in terms of required number of adders and values of cut-off frequencies of the pass and stop bands. A comparison of the proposed band-pass filter characteristics with those of a classical filter solution is provided in the paper.