Characterization of Frequency Domains of Bandlimited Frame Multiresolution Analysis

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⊂2G, ⋃m2mG≅Rd, and G\G2⋂G2+2πν≅∅(ν∈Zd).