Mixed multidimensional filters

It is shown that the basic idea to combine discrete transforms and linear difference equation filtering in the MD (multidimensional) case may be extended beyond the DFT (discrete Fourier transform) to include other types of transforms, such as the DCT (discrete cosine transform) and DHT (discrete Hartley transform). Applications of such MixeD filters have been successfully pursued for the case of 3D spatially planar signals using cone transfer functions. The computational efficiency of these MixeD filters has been confirmed elsewhere for the DFT and can be shown to carry over, by similar reasoning, to the DHT and DCT. It is noted that MixeD filter LDEs (linear difference equations) are of lower dimensionality (M-P) than for the MD LDE case, thereby simplifying design approximation (and associated stability considerations in the case of IIR (infinite impulse response) LDEs).< >