2025/02/06 by Michael Speckbacher, Speckbacher, Michael
Physics and Astronomy · #History and Developments in Astronomy #Pulsars and Gravitational Waves Research #Advanced Frequency and Time Standards
paper · pdf · doi:10.48550/arxiv.2502.04150
Given a sampling measure for the wavelet transform (resp. the short-time Fourier transform) with the wavelet (resp. window) being chosen from the family of Laguerre (resp. Hermite) functions, we provide quantitative upper bounds on the radius of any ball that does not intersect the support of the measure. The estimates depend on the condition number, i.e., the ratio of the sampling constants, but are independent of the structure of the measure. Our proofs are completely elementary and rely on explicit formulas for the respective transforms.