A New Class of Complex Compact-Supported Orthonormal Symmlets
Summary :
This paper presents a new class of complex-valued compact-supported orthonormal symmlets. Firstly, some properties of complex-valued compact-supported orthonormal symmlets are investigated, and then it is shown that complex-valued symmlets can be generated by real-valued half-band filters. Therefore, the construction of complex-valued symmlets can be reduced to the design of real-valued half-band filters. Next, a design method of real-valued half-band FIR filters with some flatness requirements is proposed. For the maximally flat half-band filters, a closed-form solution is given. For the filter design with a given degree of flatness, the design problem is formulated in the form of linear system by using the Remez exchange algorithm and considering the given flatness condition. Therefore, a set of filter coefficients can be easily computed by solving a set of linear equations, and the optimal solution is obtained through a few iterations. Finally, some design examples are presented to demonstrate the effectiveness of the proposed method.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E84-A No.7 pp.1740-1746
- Publication Date
- 2001/07/01
- Publicized
- Online ISSN
- DOI
- Type of Manuscript
- PAPER
- Category
- Digital Signal Processing
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Xi ZHANG, Toshinori YOSHIKAWA, "A New Class of Complex Compact-Supported Orthonormal Symmlets" in IEICE TRANSACTIONS on Fundamentals,
vol. E84-A, no. 7, pp. 1740-1746, July 2001, doi: .
Abstract: This paper presents a new class of complex-valued compact-supported orthonormal symmlets. Firstly, some properties of complex-valued compact-supported orthonormal symmlets are investigated, and then it is shown that complex-valued symmlets can be generated by real-valued half-band filters. Therefore, the construction of complex-valued symmlets can be reduced to the design of real-valued half-band filters. Next, a design method of real-valued half-band FIR filters with some flatness requirements is proposed. For the maximally flat half-band filters, a closed-form solution is given. For the filter design with a given degree of flatness, the design problem is formulated in the form of linear system by using the Remez exchange algorithm and considering the given flatness condition. Therefore, a set of filter coefficients can be easily computed by solving a set of linear equations, and the optimal solution is obtained through a few iterations. Finally, some design examples are presented to demonstrate the effectiveness of the proposed method.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e84-a_7_1740/_p
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@ARTICLE{e84-a_7_1740,
author={Xi ZHANG, Toshinori YOSHIKAWA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={A New Class of Complex Compact-Supported Orthonormal Symmlets},
year={2001},
volume={E84-A},
number={7},
pages={1740-1746},
abstract={This paper presents a new class of complex-valued compact-supported orthonormal symmlets. Firstly, some properties of complex-valued compact-supported orthonormal symmlets are investigated, and then it is shown that complex-valued symmlets can be generated by real-valued half-band filters. Therefore, the construction of complex-valued symmlets can be reduced to the design of real-valued half-band filters. Next, a design method of real-valued half-band FIR filters with some flatness requirements is proposed. For the maximally flat half-band filters, a closed-form solution is given. For the filter design with a given degree of flatness, the design problem is formulated in the form of linear system by using the Remez exchange algorithm and considering the given flatness condition. Therefore, a set of filter coefficients can be easily computed by solving a set of linear equations, and the optimal solution is obtained through a few iterations. Finally, some design examples are presented to demonstrate the effectiveness of the proposed method.},
keywords={},
doi={},
ISSN={},
month={July},}
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TY - JOUR
TI - A New Class of Complex Compact-Supported Orthonormal Symmlets
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1740
EP - 1746
AU - Xi ZHANG
AU - Toshinori YOSHIKAWA
PY - 2001
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E84-A
IS - 7
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - July 2001
AB - This paper presents a new class of complex-valued compact-supported orthonormal symmlets. Firstly, some properties of complex-valued compact-supported orthonormal symmlets are investigated, and then it is shown that complex-valued symmlets can be generated by real-valued half-band filters. Therefore, the construction of complex-valued symmlets can be reduced to the design of real-valued half-band filters. Next, a design method of real-valued half-band FIR filters with some flatness requirements is proposed. For the maximally flat half-band filters, a closed-form solution is given. For the filter design with a given degree of flatness, the design problem is formulated in the form of linear system by using the Remez exchange algorithm and considering the given flatness condition. Therefore, a set of filter coefficients can be easily computed by solving a set of linear equations, and the optimal solution is obtained through a few iterations. Finally, some design examples are presented to demonstrate the effectiveness of the proposed method.
ER -
English
