Obstructions for Gabor frames of the second-order B-spline Obstructions for Gabor frames of the second-order B-spline

• Published in: Advances in computational mathematics Vol. 51; no. 3
• Main Authors: Ghosh, Riya, Selvan, A. Antony
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.06.2025; Springer Nature B.V
• Subjects: Computational Mathematics and Numerical Analysis; Computational Science and Engineering; Hyperbolas; Lattice parameters; Mathematical and Computational Biology; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Obstructions; Time-frequency analysis; Visualization; Zak transform; 42C40; Shift-invariant spaces; Zibulski–Zeevi matrix; Laurent operator; Gabor frames; Primary 42C15; B-splines

For a window g ∈ L 2 ( R ) , the subset of all lattice parameters ( a , b ) ∈ R + 2 such that G ( g , a , b ) = { e 2 π i b m · g ( · - a k ) : k , m ∈ Z } forms a frame for L 2 ( R ) is known as the frame set of g . In time-frequency analysis, determining the Gabor frame set for a given window is a...