Characterization of Frequency Domains of Bandlimited Frame Multiresolution Analysis

Zhihua Zhang
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Zhihua Zhang: School of Mathematics, Shandong University, Jinan 250100, China

Mathematics, 2021, vol. 9, issue 9, 1-9

Abstract: Framelets have been widely used in narrowband signal processing, data analysis, and sampling theory, due to their resilience to background noise, stability of sparse reconstruction, and ability to capture local time-frequency information. The well-known approach to construct framelets with useful properties is through frame multiresolution analysis (FMRA). In this article, we characterize the frequency domain of bandlimited FMRAs: there exists a bandlimited FMRA with the support of frequency domain G if and only if G satisfies G ? 2 G , ? m 2 m G ? R d , and G \ G 2 ? G 2 + 2 ? ? ? ? ( ? ? Z d ) .

Keywords: framelets; bandlimited multiresolution analysis; frequency domain (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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