Polyphase matrix and lattice decomposition for multirate filters and filter banks

A novel formula is derived for the decomposition of a digital filter into a matrix or lattice of subfilters, with conventional polyphase decomposition as a special case. This generic polyphase decomposition formula provides unified approaches for multirate filters and filter banks. The decomposition of subfilters can be fully automated, therefore replacing many ad hoc, tedious, and error-prone design and optimization procedures. Two novel structures are obtained for one-dimensional digital signal processing, a polyphase filter that is a sampling rate converter plus a variable fractional sample phase shifter, and a polyphase-matrix-FFT filter bank that is capable of a rational decimation rate and includes the most efficient filter banks as special cases