Explicit Formula for Predictive FIR Filters and Differentiators Using Hahn Orthogonal Polynomials
Summary :
An explicit expression for the impulse response coefficients of the predictive FIR digital filters is derived. The formula specifies a four-parameter family of smoothing FIR digital filters containing the Savitsky-Goaly filters, the Heinonen-Neuvo polynomial predictors, and the smoothing differentiators of arbitrary integer orders. The Hahn polynomials, which are orthogonal with respect to a discrete variable, are the main tool employed in the derivation of the formula. A recursive formula for the computation of the transfer function of the filters, which is the z-transform of a terminated sequence of polynomial ordinates, is also introduced. The formula can be used to design structures with low computational complexity for filters of any order.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E90-A No.8 pp.1511-1518
- Publication Date
- 2007/08/01
- Publicized
- Online ISSN
- 1745-1337
- DOI
- 10.1093/ietfec/e90-a.8.1511
- Type of Manuscript
- Special Section PAPER (Special Section on Papers Selected from the 21st Symposium on Signal Processing)
- Category
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Saed SAMADI, Akinori NISHIHARA, "Explicit Formula for Predictive FIR Filters and Differentiators Using Hahn Orthogonal Polynomials" in IEICE TRANSACTIONS on Fundamentals,
vol. E90-A, no. 8, pp. 1511-1518, August 2007, doi: 10.1093/ietfec/e90-a.8.1511.
Abstract: An explicit expression for the impulse response coefficients of the predictive FIR digital filters is derived. The formula specifies a four-parameter family of smoothing FIR digital filters containing the Savitsky-Goaly filters, the Heinonen-Neuvo polynomial predictors, and the smoothing differentiators of arbitrary integer orders. The Hahn polynomials, which are orthogonal with respect to a discrete variable, are the main tool employed in the derivation of the formula. A recursive formula for the computation of the transfer function of the filters, which is the z-transform of a terminated sequence of polynomial ordinates, is also introduced. The formula can be used to design structures with low computational complexity for filters of any order.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1093/ietfec/e90-a.8.1511/_p
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@ARTICLE{e90-a_8_1511,
author={Saed SAMADI, Akinori NISHIHARA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Explicit Formula for Predictive FIR Filters and Differentiators Using Hahn Orthogonal Polynomials},
year={2007},
volume={E90-A},
number={8},
pages={1511-1518},
abstract={An explicit expression for the impulse response coefficients of the predictive FIR digital filters is derived. The formula specifies a four-parameter family of smoothing FIR digital filters containing the Savitsky-Goaly filters, the Heinonen-Neuvo polynomial predictors, and the smoothing differentiators of arbitrary integer orders. The Hahn polynomials, which are orthogonal with respect to a discrete variable, are the main tool employed in the derivation of the formula. A recursive formula for the computation of the transfer function of the filters, which is the z-transform of a terminated sequence of polynomial ordinates, is also introduced. The formula can be used to design structures with low computational complexity for filters of any order.},
keywords={},
doi={10.1093/ietfec/e90-a.8.1511},
ISSN={1745-1337},
month={August},}
Copy
TY - JOUR
TI - Explicit Formula for Predictive FIR Filters and Differentiators Using Hahn Orthogonal Polynomials
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1511
EP - 1518
AU - Saed SAMADI
AU - Akinori NISHIHARA
PY - 2007
DO - 10.1093/ietfec/e90-a.8.1511
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E90-A
IS - 8
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - August 2007
AB - An explicit expression for the impulse response coefficients of the predictive FIR digital filters is derived. The formula specifies a four-parameter family of smoothing FIR digital filters containing the Savitsky-Goaly filters, the Heinonen-Neuvo polynomial predictors, and the smoothing differentiators of arbitrary integer orders. The Hahn polynomials, which are orthogonal with respect to a discrete variable, are the main tool employed in the derivation of the formula. A recursive formula for the computation of the transfer function of the filters, which is the z-transform of a terminated sequence of polynomial ordinates, is also introduced. The formula can be used to design structures with low computational complexity for filters of any order.
ER -
English
