Author:

Keywords:

Science & Technology, Technology, Physical Sciences, Life Sciences & Biomedicine, Computer Science, Interdisciplinary Applications, Engineering, Electrical & Electronic, Mathematics, Applied, Optics, Physics, Applied, Radiology, Nuclear Medicine & Medical Imaging, Computer Science, Engineering, Mathematics, Physics, COSINE CROSSINGS, BAR-DAVID THEOREM, WAVELET TRANSFORM, IMPLICIT SAMPLING, SPLINES, 4006 Communications engineering, 4009 Electronics, sensors and digital hardware, 5102 Atomic, molecular and optical physics

Abstract:

The sampling theorem of Bar-David provides an implicit representation of bandlimited signals using their crossings with a cosine function. This cosine function is chosen in a way that guarantees a unique representation of the signal. Previously, we extended Bar-David's theorem to periodic functions on an interval, leading to a multiplicative representation involving a Riesz product whose roots form a unique and stable representation of the signal. We also presented numerical algorithms for the analysis and synthesis of 1D signals. In this paper, we extend our previous results by developing algorithms for 2D signals and incorporating the wavelet transform into the cosine crossing representation.