Convolution Theorems for Two-Dimensional LCT of Angularly Periodic Functions in Polar Coordinates

By focusing on a special type of functions that are angularly periodic with period 2π, a relationship between two-dimensional (2-D) linear canonical transform (LCT) and linear canonical Hankel transform (LCHT) is disclosed, implying that the mapping from the nth Fourier coefficient of the original function to that of its 2-D LCT version is an nth-order LCHT. In view of this relation, three kinds of convolution theorems for the 2-D LCT in polar coordinates are proposed. The equivalence of the multiplicative filter models derived is also illustrated.