Transitional Selective Linear Phase 1D FIR Filter Function Generated by Christoffel-Darboux Formula for Chebyshev Polynomials

In this paper we propose a new economical selective low-pass finite impulse response filter function. First, we describe the two types of already developed filters, and then we obtain three new different types of filters, by combining the previous ones. Also, the general form of the proposed filter is given. In order to verify the effectiveness of the proposed filter function, the cut-off frequencies of the stop-band and pass-band of the filter, for equal constant group delay, are analysed and compared with classical first and second type of filters. It is shown that proposed filter is efficient related to high selectivity and high values of attenuation in the stop-band of the filter. Index Terms--Difference equations, digital filters, filtering theory, finite impulse response filter.