2018/06/14 by A. Ganiou D. Atindehou, Atindehou, A. Ganiou D., Christina Frederick +5
Computer Science · Mathematics · #42C15 #42C40 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Image and Signal Denoising Methods #Mathematical Analysis and Transform Methods
paper · pdf · doi:10.48550/arxiv.1806.05614
openalex publication_date 2018/06/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The frame set of a function g∈ L2(ℝ) is the set of all parameters (a, b)∈ ℝ2+ for which the collection of time-frequency shifts of g along aℤ× bℤ form a Gabor frame for L2(ℝ). Finding the frame set of a given function remains a challenging open problem in time-frequency analysis. In this paper, we establish new regions of the frame set of the second order B-spline. Our method relies on the compact support of this function to partition a subset of the putative frame set and find an explicit dual window function in each of the partition regions. Numerical evidence indicates the existence of further points belonging to the frame set.