Regular multidimensional linear phase FIR digital filter banks and wavelet bases

Abstract

Design methods for regular multidimensional perfect reconstruction (PR) filter banks are described. A systematic method for two-channel and four-channel filter banks is presented. The main novelties are: (1) the filters have impulse response with square support, rather than diamond support, (2) regular designs that have rectangular support are also presented, which are highly efficient in practice, since expensive memory is saved; (3) in addition to new diamond filters for the two-channel case, hexagonally-symmetric filters are also derived; and (4) novel 3-D filter banks are also designed. In all cases the filters are linear phase, achieve arbitrarily high regularity and can be used to obtain biorthogonal wavelet bases. The filter banks can be implemented in a structurally perfect-reconstruction manner.