Two-dimensional OLCT of angularly periodic functions in polar coordinates

Searching for novel signal processing theories and methods has always been a research hotspot in the field of modern signal processing. The existing transform methods for dealing with non-stationary signals are based on traditional Cartesian coordinates, which are very inconvenient to deal with signals naturally described by polar coordinates. This paper studies two-dimensional offset linear canonical transform (OLCT) in polar coordinates. Firstly, the definition of the two-dimensional OLCT in polar coordinates is proposed, and the offset linear canonical Hankel transform (OLCHT) formula is derived. Secondly, the relationship between the OLCT and the OLCHT is revealed through the angular periodic function. Then, some properties of the two-dimensional OLCT in polar coordinates are proved based on the mentioned relationship. Finally, the proposed two-dimensional OLCT is applied in the computed tomography. The effectiveness and feasibility of the proposed method are verified by simulation experiments.