Solving the Selesnick-Burrus Filter Design Equations Using Computational Algebra and Algebraic Geometry
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arXiv
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| Formato: | Preprint |
| Publicado: |
2002
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| _version_ | 1866909853373431808 |
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| author | Little, John B. |
| author_facet | Little, John B. |
| contents | In a recent paper, I. Selesnick and C.S. Burrus developed a design method for maximally flat FIR low-pass digital filters with reduced group delay. Their approach leads to a system of polynomial equations depending on three integer design parameters $K,L,M$. In certain cases (their ``Region I''), Selesnick and Burrus were able to derive solutions using only linear algebra; for the remaining cases ("Region II''), they proposed using Gröbner bases. This paper introduces a different method, based on multipolynomial resultants, for analyzing and solving the Selesnick-Burrus design equations. The results of calculations are presented, and some patterns concerning the number of solutions as a function of the design parameters are proved. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_math_0209248 |
| institution | arXiv |
| publishDate | 2002 |
| record_format | arxiv |
| spellingShingle | Solving the Selesnick-Burrus Filter Design Equations Using Computational Algebra and Algebraic Geometry Little, John B. Numerical Analysis Commutative Algebra Algebraic Geometry Classical Analysis and ODEs 94A12; 13P99 In a recent paper, I. Selesnick and C.S. Burrus developed a design method for maximally flat FIR low-pass digital filters with reduced group delay. Their approach leads to a system of polynomial equations depending on three integer design parameters $K,L,M$. In certain cases (their ``Region I''), Selesnick and Burrus were able to derive solutions using only linear algebra; for the remaining cases ("Region II''), they proposed using Gröbner bases. This paper introduces a different method, based on multipolynomial resultants, for analyzing and solving the Selesnick-Burrus design equations. The results of calculations are presented, and some patterns concerning the number of solutions as a function of the design parameters are proved. |
| title | Solving the Selesnick-Burrus Filter Design Equations Using Computational Algebra and Algebraic Geometry |
| topic | Numerical Analysis Commutative Algebra Algebraic Geometry Classical Analysis and ODEs 94A12; 13P99 |
| url | https://arxiv.org/abs/math/0209248 |