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Minimum-energy wavelet frame on the interval

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Abstract

The construction and properties of interval minimum-energy wavelet frame are systematically studied in this paper. They are as follows: 1) give the definition of interval minimum-energy wavelet frame; 2) give the necessary and sufficient conditions for the minimum-energy frames for L 2[0,1]; 3) present the construction algorithm for minimum-energy wavelet frame associated with refinable functions on the interval with any support γ; 4) give the decomposition and reconstruction formulas of the minimum-energy frame on the interval [0,1].

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Authors and Affiliations

  1. College of Information and Engineering, Xiangtan University, Xiangtan, 411105, China

    XiePing Gao & ChunHong Cao

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  1. XiePing Gao
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  2. ChunHong Cao
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Correspondence to ChunHong Cao.

Additional information

Supported by the National Natural Science Foundation of China (Grant No. 60375021), the Natural Science Foundation of Hunan Province, China (Grant No. 05JJ10011), and the Scientific Research Fund of Hunan Provincial Education Department of China (Grant Nos. 04A056 and 06C836)

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Gao, X., Cao, C. Minimum-energy wavelet frame on the interval. Sci. China Ser. F-Inf. Sci. 51, 1547–1562 (2008). https://doi.org/10.1007/s11432-008-0107-0

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  • DOI: https://doi.org/10.1007/s11432-008-0107-0

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