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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 -