On efficient implementation of multidimensional multirate filters derived from one-dimensional filters

We study the efficient implementation of multidimensional (MD) filters used in multirate systems. These filters, typically having parallelepiped-shaped passband supports, can be derived from one-dimensional (1D) prototype filters. The resulting nonseparable MD filters have separable polyphase components that are combinations of the polyphase components of the 1D prototypes, so efficient implementation exists. We show that, for the two-dimensional case, all the polyphase components of the 1D prototypes are utilized. Therefore, there is no design overhead in this scheme.