Adaptive Sampling for Signals Associated with the Special Affine Fourier Transform.

Jiang, Yingchun; Li, Yujie; Yang, Jing

Adaptive sampling is inspired by the working principle of biological neurons, which converts the amplitude information of the received signal into a time sequence through a time encoding machine (TEM). The article mainly studies uniform sampling and adaptive sampling of non-bandlimited signals in two kinds of function spaces associated with the special affine Fourier transform (SAFT). Firstly, based on the stability characterization of the basis functions, we prove the existence of orthogonal projection operators in function spaces associated with the canonical convolution and the SAFT-convolution, respectively. Secondly, uniform sampling theorems are established for two kinds of signals living in the proposed function spaces. Finally, adaptive sampling schemes based on the crossing TEM and the integrate-and-fire TEM are studied. Moreover, the corresponding iterative reconstruction algorithms with exponential convergence are provided.

SAMPLING theorem; FUNCTION spaces; ORTHOGRAPHIC projection; FOURIER transforms; SIGNAL sampling

Numerical Functional Analysis & Optimization, 2024, Vol 45, Issue 12, p599

0163-0563

Academic Journal

10.1080/01630563.2024.2405471