Sampling theorems in the OLCT and the OLCHT domains by polar coordinates

Abstract

The sampling theorem for the offset linear canonical transform (OLCT) of bandlimited functions in polar coordinates is an important mathematical tool in many fields of signal processing and medical imaging. This paper investigates two sampling theorems for interpolating \Omega bandlimited and highest frequency bandlimited functions f(r,{\theta}) in the OLCT and the offset linear canonical Hankel transform (OLCHT) domains by polar coordinates. Based on the classical Stark's interpolation formulas, we derive the sampling theorems for \Omega bandlimited functions f(r,{\theta}) in the OLCT and the OLCHT domains, respectively. The first interpolation formula is concise and applicable. Due to the consistency of the OLCHT order, the second interpolation formula is superior to the first interpolation formula in computational complexity.Comment: 24 page