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Abstract <p> Constructive necessary and sufficient conditions for a family of periodic wavelets to form a Parseval frame are obtained. The presented criterion generalizes the unitary and oblique extension principles. The case of a single wavelet generator and the situation in which the refinable functions are trigonometric polynomials are discussed in detail. </p>

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Criteria for Periodic Wavelet Frames

  • 期刊论文

  • 发表日期：

    2025年8月1日

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  • A. A. Gorshanova,
  • E. A. Lebedeva

摘要

Abstract

Constructive necessary and sufficient conditions for a family of periodic wavelets to form a Parseval frame are obtained. The presented criterion generalizes the unitary and oblique extension principles. The case of a single wavelet generator and the situation in which the refinable functions are trigonometric polynomials are discussed in detail.