Design Method for Low-Delay Maximally Flat FIR Digital Differentiators with Variable Stopbands Obtained by Minimizing Lp Norm
Summary :
Linear phase maximally flat digital differentiators (DDs) with stopbands obtained by minimizing the Lp norm are filters with important practical applications, as they can differentiate input signals without distortion. Stopbands designed by minimizing the Lp norm can be used to control the relationship between the steepness in the transition band and the ripple scale. However, linear phase DDs are unsuitable for real-time processing because each group delay is half of the filter order. In this paper, we proposed a design method for a low-delay maximally flat low-pass/band-pass FIR DDs with stopbands obtained by minimizing the Lp norm. The proposed DDs have low-delay characteristics that approximate the linear phase characteristics only in the passband. The proposed transfer function is composed of two functions, one with flat characteristics in the passband and one that ensures the transfer function has Lp approximated characteristics in the stopband. In the optimization of the latter function, Newton's method is employed.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E100-A No.7 pp.1513-1521
- Publication Date
- 2017/07/01
- Publicized
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.E100.A.1513
- Type of Manuscript
- PAPER
- Category
- Digital Signal Processing
Authors
Ryosuke KUNII
Tokyo University of Science
Takashi YOSHIDA
Tokyo University of Science
Naoyuki AIKAWA
Tokyo University of Science
Keyword
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Ryosuke KUNII, Takashi YOSHIDA, Naoyuki AIKAWA, "Design Method for Low-Delay Maximally Flat FIR Digital Differentiators with Variable Stopbands Obtained by Minimizing Lp Norm" in IEICE TRANSACTIONS on Fundamentals,
vol. E100-A, no. 7, pp. 1513-1521, July 2017, doi: 10.1587/transfun.E100.A.1513.
Abstract: Linear phase maximally flat digital differentiators (DDs) with stopbands obtained by minimizing the Lp norm are filters with important practical applications, as they can differentiate input signals without distortion. Stopbands designed by minimizing the Lp norm can be used to control the relationship between the steepness in the transition band and the ripple scale. However, linear phase DDs are unsuitable for real-time processing because each group delay is half of the filter order. In this paper, we proposed a design method for a low-delay maximally flat low-pass/band-pass FIR DDs with stopbands obtained by minimizing the Lp norm. The proposed DDs have low-delay characteristics that approximate the linear phase characteristics only in the passband. The proposed transfer function is composed of two functions, one with flat characteristics in the passband and one that ensures the transfer function has Lp approximated characteristics in the stopband. In the optimization of the latter function, Newton's method is employed.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E100.A.1513/_p
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@ARTICLE{e100-a_7_1513,
author={Ryosuke KUNII, Takashi YOSHIDA, Naoyuki AIKAWA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Design Method for Low-Delay Maximally Flat FIR Digital Differentiators with Variable Stopbands Obtained by Minimizing Lp Norm},
year={2017},
volume={E100-A},
number={7},
pages={1513-1521},
abstract={Linear phase maximally flat digital differentiators (DDs) with stopbands obtained by minimizing the Lp norm are filters with important practical applications, as they can differentiate input signals without distortion. Stopbands designed by minimizing the Lp norm can be used to control the relationship between the steepness in the transition band and the ripple scale. However, linear phase DDs are unsuitable for real-time processing because each group delay is half of the filter order. In this paper, we proposed a design method for a low-delay maximally flat low-pass/band-pass FIR DDs with stopbands obtained by minimizing the Lp norm. The proposed DDs have low-delay characteristics that approximate the linear phase characteristics only in the passband. The proposed transfer function is composed of two functions, one with flat characteristics in the passband and one that ensures the transfer function has Lp approximated characteristics in the stopband. In the optimization of the latter function, Newton's method is employed.},
keywords={},
doi={10.1587/transfun.E100.A.1513},
ISSN={1745-1337},
month={July},}
Copy
TY - JOUR
TI - Design Method for Low-Delay Maximally Flat FIR Digital Differentiators with Variable Stopbands Obtained by Minimizing Lp Norm
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1513
EP - 1521
AU - Ryosuke KUNII
AU - Takashi YOSHIDA
AU - Naoyuki AIKAWA
PY - 2017
DO - 10.1587/transfun.E100.A.1513
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E100-A
IS - 7
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - July 2017
AB - Linear phase maximally flat digital differentiators (DDs) with stopbands obtained by minimizing the Lp norm are filters with important practical applications, as they can differentiate input signals without distortion. Stopbands designed by minimizing the Lp norm can be used to control the relationship between the steepness in the transition band and the ripple scale. However, linear phase DDs are unsuitable for real-time processing because each group delay is half of the filter order. In this paper, we proposed a design method for a low-delay maximally flat low-pass/band-pass FIR DDs with stopbands obtained by minimizing the Lp norm. The proposed DDs have low-delay characteristics that approximate the linear phase characteristics only in the passband. The proposed transfer function is composed of two functions, one with flat characteristics in the passband and one that ensures the transfer function has Lp approximated characteristics in the stopband. In the optimization of the latter function, Newton's method is employed.
ER -
English
