2008/08/10 by Vincenza Del Prete, Del Prete, Vincenza
Computer Science · Mathematics · #42C15 #46E20 #46E22 #Digital Filter Design and Implementation #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods
paper · pdf · doi:10.48550/arxiv.0808.1412
openalex publication_date 2008/08/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this article we obtain families of frames for the space Bωof functions with band in [-ω,ω] by using the theory of shift-invariant spaces. Our results are based on the Gramian analysis of A. Ron and Z. Shen and a variant, due to Bownik, of their characterization of families of functions whose shifts form frames or Riesz bases. We give necessary and sufficient conditions for the translates of a finite number of functions (generators) to be a frame or a Riesz basis for Bω. We also give explicit formulas for the dual generators and we apply them to Hilbert transform sampling and derivative sampling. Finally, we provide numerical experiments which support the theory.