The two-dimensional OLCT of angularly periodic functions in polar coordinates

The two-dimensional (2D) offset linear canonical transform (OLCT) in polar coordinates plays an important role in many fields of optics and signal processing. This paper studies the 2D OLCT in polar coordinates. Firstly, we extend the 2D OLCT to the polar coordinate system, and obtain the offset linear canonical Hankel transform (OLCHT) formula. Secondly, through the angular periodic function with a period of 2{\pi}, the relationship between the 2D OLCT and the OLCHT is revealed. Finally, the spatial shift and convolution theorems for the 2D OLCT are proposed by using this relationship.