IEICE TRANSACTIONS on Fundamentals
Parallel and Modular Structures for FIR Digital Filters
Summary :
The scope of this paper is the realization of FIR digital filters with an emphasis on linear phase and maximally flat cases. The transfer functions of FIR digital filters are polynomials and polynomial evaluation algorithms can be utilized as realization schemes of these filters. In this paper we investigate the application of a class of polynomial evaluation algorithms called "recursive triangles" to the realization of FIR digital filters. The realization of an arbitrary transfer function using De Casteljau algorithm, a member of the recursive triangles used for evaluating Bernstein polynomials, is studied and it is shown that in some special and important cases it yields efficient modular structures. Realization of two dimensional filters based on Bernstein approximation is also considered. We also introduce recursive triangles for evaluating the power basis representation of polynomials and give a new multiplier-less maximally flat structure based on them. Finally, we generalize the structure further and show that Chebyshev polynomials can also be evaluated by the triangles. This is the triangular counterpart of the well-known Chebyshev structure. In general,the triangular structures yield highly modular digital filters that can be mapped to an array of concurrent processors resulting in high speed and effcient filtering specially for maximally flat transfer functions.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E77-A No.3 pp.467-474
- Publication Date
- 1994/03/25
- Publicized
- Online ISSN
- DOI
- Type of Manuscript
- Special Section PAPER (Special Section on the 6th Karuizawa Workshop on Circuits and Systems)
- Category
- Digital Signal Processing
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Saed SAMADI, Akinori NISHIHARA, Nobuo FUJII, "Parallel and Modular Structures for FIR Digital Filters" in IEICE TRANSACTIONS on Fundamentals,
vol. E77-A, no. 3, pp. 467-474, March 1994, doi: .
Abstract: The scope of this paper is the realization of FIR digital filters with an emphasis on linear phase and maximally flat cases. The transfer functions of FIR digital filters are polynomials and polynomial evaluation algorithms can be utilized as realization schemes of these filters. In this paper we investigate the application of a class of polynomial evaluation algorithms called "recursive triangles" to the realization of FIR digital filters. The realization of an arbitrary transfer function using De Casteljau algorithm, a member of the recursive triangles used for evaluating Bernstein polynomials, is studied and it is shown that in some special and important cases it yields efficient modular structures. Realization of two dimensional filters based on Bernstein approximation is also considered. We also introduce recursive triangles for evaluating the power basis representation of polynomials and give a new multiplier-less maximally flat structure based on them. Finally, we generalize the structure further and show that Chebyshev polynomials can also be evaluated by the triangles. This is the triangular counterpart of the well-known Chebyshev structure. In general,the triangular structures yield highly modular digital filters that can be mapped to an array of concurrent processors resulting in high speed and effcient filtering specially for maximally flat transfer functions.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e77-a_3_467/_p
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@ARTICLE{e77-a_3_467,
author={Saed SAMADI, Akinori NISHIHARA, Nobuo FUJII, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Parallel and Modular Structures for FIR Digital Filters},
year={1994},
volume={E77-A},
number={3},
pages={467-474},
abstract={The scope of this paper is the realization of FIR digital filters with an emphasis on linear phase and maximally flat cases. The transfer functions of FIR digital filters are polynomials and polynomial evaluation algorithms can be utilized as realization schemes of these filters. In this paper we investigate the application of a class of polynomial evaluation algorithms called "recursive triangles" to the realization of FIR digital filters. The realization of an arbitrary transfer function using De Casteljau algorithm, a member of the recursive triangles used for evaluating Bernstein polynomials, is studied and it is shown that in some special and important cases it yields efficient modular structures. Realization of two dimensional filters based on Bernstein approximation is also considered. We also introduce recursive triangles for evaluating the power basis representation of polynomials and give a new multiplier-less maximally flat structure based on them. Finally, we generalize the structure further and show that Chebyshev polynomials can also be evaluated by the triangles. This is the triangular counterpart of the well-known Chebyshev structure. In general,the triangular structures yield highly modular digital filters that can be mapped to an array of concurrent processors resulting in high speed and effcient filtering specially for maximally flat transfer functions.},
keywords={},
doi={},
ISSN={},
month={March},}
Copy
TY - JOUR
TI - Parallel and Modular Structures for FIR Digital Filters
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 467
EP - 474
AU - Saed SAMADI
AU - Akinori NISHIHARA
AU - Nobuo FUJII
PY - 1994
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E77-A
IS - 3
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - March 1994
AB - The scope of this paper is the realization of FIR digital filters with an emphasis on linear phase and maximally flat cases. The transfer functions of FIR digital filters are polynomials and polynomial evaluation algorithms can be utilized as realization schemes of these filters. In this paper we investigate the application of a class of polynomial evaluation algorithms called "recursive triangles" to the realization of FIR digital filters. The realization of an arbitrary transfer function using De Casteljau algorithm, a member of the recursive triangles used for evaluating Bernstein polynomials, is studied and it is shown that in some special and important cases it yields efficient modular structures. Realization of two dimensional filters based on Bernstein approximation is also considered. We also introduce recursive triangles for evaluating the power basis representation of polynomials and give a new multiplier-less maximally flat structure based on them. Finally, we generalize the structure further and show that Chebyshev polynomials can also be evaluated by the triangles. This is the triangular counterpart of the well-known Chebyshev structure. In general,the triangular structures yield highly modular digital filters that can be mapped to an array of concurrent processors resulting in high speed and effcient filtering specially for maximally flat transfer functions.
ER -
English
