Polyphase Decomposition of Digital Fractional-Delay Filters

Abstract

This letter shows that, for arbitrary $M$ -fold polyphase decompositions, the polyphase components of digital fractional-delay (FD) filters correspond to FD filters as well, but with different delays and gains. For even values of $M$ , the components also have additional and different phase offsets. The letter also discusses the application of these results to the optimization of high-order filters with few unknowns.