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

Abstract

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.

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

“…For N = 6, the impulse response coefficients, h(N =6,r, k), are given by matrix form (10). (see 10)For N = 7, the impulse response coefficients, h(N =7,r, k), are given by matrix form (11). (see 11)The impulse response characteristics for N = 5 and N = 12, respectively, are presented in Fig.…”

“…Low complexity realisation scheme of the new classes of low-pass multiplierless linear-phase FIR filter functions have been described in papers [9][10][11][12][13][14][15][16].…”

Analysis of finite tolerance effect of critical pole on characteristics of selective RC active special Gegenbauer filters

“…CHRISTOFFEL-DARBOUX formula, [1,2], can be efficiently implemented in filter function synthesis in continuous domain, as described by analytical method in works [3][4][5][6]. Related results in application of the Christoffel-Darboux formula in design of onedimensional z domain multiplierless linear-phase FIR filters and 2D FIR filter have also been reported in works [7][8][9][10][11][12]. Popular one dimensional multiplierless CIC filters are described in literature [13,14].…”