Characterization of Frequency Domains of Bandlimited Frame Multiresolution Analysis

Mathematics

Zhihua Zhang¹ 

[1] School of Mathematics, Shandong University, Jinan 250100, China;

关键词: framelets;    bandlimited multiresolution analysis;    frequency domain;   

DOI  :  10.3390/math9091050

来源: DOAJ

【 摘 要 】

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 $G\subset 2G$, ${\bigcup }_m{2}^{m}G\cong {\mathbb{R}}^d$, and $\left(G\backslash \frac{G}{2}\right)\bigcap \left(\frac{G}{2}+2\pi \mathit{\nu }\right)\cong \varnothing (\mathit{\nu }\in {\mathbb{Z}}^d)$.

【 授权许可】

Unknown