Abstract
Abstract In this paper, we study minimum-energy frame Ψ = {ψ1, ψ2, … , ψN} with arbitrary integer dilation factor d for L2(R), Ψ correspond to some refinable functions with compact support. A precise existence criterion of Ψ is given in terms of an inequality condition on the Laurent polynomial symbols of the refinable functions. We give a constructive proof that when Ψ does exist, d functions with compact support are sufficient to constitute Ψ, and present a explicit formula of constructing Ψ. Finally, we present the minimum-energy frames decomposition and reconstruction formulas which are similar to those of orthogonal wavelets. Numerical examples are given.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
