1998/12/30 by Peter G. Casazza, Casazza, Peter G., Ole Christensen +1 · 5 citations
Computer Science · Earth and Planetary Sciences · Mathematics · #46B07 #46C05 #FOS: Mathematics #Functional Analysis (math.FA) #Image and Signal Denoising Methods #Mathematical Analysis and Transform Methods #Mathematics #Seismic Imaging and Inversion Techniques #math.FA #msc:46B07 #msc:46C05
paper · pdf · doi:10.48550/arxiv.math/9812159
published in arXiv (Cornell University) (Cornell University) · 11 pages
arxiv created 1998/12/30 · openalex publication_date 1998/12/30 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
A Weyl-Heisenberg frame for L2(R) is a frame consisting of translates and modulates of a fixed function. In this paper we give necessary and sufficient conditions for this family to form a tight WH-frame. This allows us to write down explicitly all functions g for which all translates and modulates of g form an orthonormal basis for L2(R). There are a number of consequences of this classification, including a simple direct classification of the alternate dual frames to a WH-frame (A result originally due to Janssen).