Generating 2-D FIR filter functions by Christoffel-Darboux formula for Chebyshev polynomials of the second kind

Global Christoffel-Darboux formula for different polynomials has already been used for the filter design. Here, this formula for orthonormal Chebyshev polynomials of the second kind and for two independent variables is applied in generating novel class linear-phase two-dimensional (2-D) finite impul...

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Bibliographic Details
Published in:International journal of electronics 2017-03, Vol.104 (3), p.416-432
Main Authors: Ciric, Dejan G, Pavlovic, Vlastimir D, Doncov, Nebojsa S
Format: Article
Language:English
Subjects:
Approximation
Chebyshev approximation
Chebyshev classical orthonormal polynomials of the second kind
Christoffel-Darboux formula
Digital filters
Economics
Electrical engineering
Electronics
Functions (mathematics)
Linear-phase 2-D FIR filter
Mathematical analysis
Polynomials
symmetric filter
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Summary:Global Christoffel-Darboux formula for different polynomials has already been used for the filter design. Here, this formula for orthonormal Chebyshev polynomials of the second kind and for two independent variables is applied in generating novel class linear-phase two-dimensional (2-D) finite impulse response (FIR) digital filter functions. In this way, 2-D filters with some specific features including economy, phase linearity, symmetry and selectivity are designed. Representative examples of the 2-D FIR digital filters of a new class obtained by the proposed approximation technique are given. A filter generated by the proposed approach is compared with the corresponding one generated by the procedure from literature.
ISSN:0020-7217
1362-3060
DOI:10.1080/00207217.2016.1218061