Multidimensional filtering using combined discrete Fourier transform and linear difference equation methods

A technique is proposed for filtering multidimensional (MD) discrete signals that combines discrete Fourier transform (DFT) and linear difference equation (LDE) methods. A partial P-dimensional DFT (P<M) is applied to the input signal, and then each P-dimensional complex frequency point is subjected to complex (M-P)-dimensional LDE filtering, followed by inverse partial P-dimensional DFT of the outputs of the LDE filters. The result is a MD filter that, at least for M=2 and M=3, is easier to design than LDE filters and lends itself to real-time implementation. The method is shown by example to be computationally more efficient than DFT or LDE methods for the implementation of a comparable 3-dimensional filter, where a 3-dimensional LDE filter of order (4,4,4) is used for the comparison