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

Authors

  • V. D. Pavlovic University of Niš
  • D. G. Ciric University of Niš
  • N. S. Doncov University of Niš

DOI:

https://doi.org/10.5755/j01.eee.18.8.2639

Keywords:

Difference equations, digital filters, filtering theory, finite impulse response filter

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 digital finite impulse response (FIR) filter function is generated in compact explicit form. In addition, a new difference equation and structure of linear phase digital FIR filter are proposed. Two examples of the extremely economic FIR filter (with four adders and without multipliers) designed by the proposed technique are presented. The proposed solutions are extremely efficiency in regard to energy consumption.

DOI: http://dx.doi.org/10.5755/j01.eee.18.8.2639

Downloads

Published

2012-10-17

How to Cite

Pavlovic, V. D., Ciric, D. G., & Doncov, N. S. (2012). Christoffel-Darboux Formula Most Directly Applied in Generating Economical Linear Phase Low-Pass Digital FIR Filter Functions. Elektronika Ir Elektrotechnika, 18(8), 109-112. https://doi.org/10.5755/j01.eee.18.8.2639

Issue

Vol. 18 No. 8 (2012)

Section

TELECOMMUNICATIONS ENGINEERING

License

The copyright for the paper in this journal is retained by the author(s) with the first publication right granted to the journal. The authors agree to the Creative Commons Attribution 4.0 (CC BY 4.0) agreement under which the paper in the Journal is licensed.

By virtue of their appearance in this open access journal, papers are free to use with proper attribution in educational and other non-commercial settings with an acknowledgement of the initial publication in the journal.