Applications of complex filters to realize three-dimensonal combined DFT/LDE transfer functions

The recently proposed method of combined discrete Fourier transform (DFT)/linear difference equation (LDE) filtering of three-dimensional (3-D) spatio-temporal signals employs LDE's with real coefficients. It is shown here that the real-coefficient LDE's impose transfer function symmetries that prevent the 3-D filter from distinguishing between 3-D input signals having reflective symmetry in the direction of the LDE filtering. These transfer function symmetry constraints are relaxed by using complex-coefficient LDE's.