Christoffel-Darboux Formula Most Directly Applied in Generating Economical Linear Phase Low-Pass Digital FIR Filter Functions

V. D. Pavlovic, D. G. Ciric, N. S. Doncov
2012 Elektronika ir Elektrotechnika  
 Abstract-The approximation problem of a filter function of even and odd order is solved mathematically in this paper most directly applying the proposed Christoffel-Darboux formula for two continual orthogonal polynomials on the equal finite segment. As a result, a linear phase low-pass digital finite impulse response (FIR) filter function is generated in compact explicit form. In addition, a new difference equation and structure of digital FIR filter are proposed. Two examples of the
more » ... ples of the extremely economic FIR filters (with four adders and without multipliers) designed by the proposed technique are presented. The proposed solutions are efficient in regard to energy consumption and have a high selectivity. Index Terms-Difference equations, digital filters, filtering theory, finite impulse response filter.
doi:10.5755/j01.eee.18.8.2639 fatcat:fwmh4pfuiveybngwdg7posrstu