Polyphase Decomposition of Digital Fractional-Delay Filters

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.