K-cyclic symmetries in multidimensional sampled signals

In this paper, K-cyclic frequency domain symmetry conditions for N-dimensional sampled signals are introduced. It is shown that these frequency domain symmetry conditions result in certain interrelationships between the sample values. A theorem is given that specifies these interrelationships. Several interesting properties of K-cyclic symmetries are discussed. Also, a systematic approach is given for finding the parameters of several commonly encountered symmetry conditions. Certain implications to multidimensional digital filtering are discussed, including Lpoptimality and the reduction in computation for design and implementation.