Generalized adaptive polyphase algorithm

The polyphase (PPS) algorithm discussed by Iyer et al. (see Proc. ICASSP, 1994) offers a very attractive solution to the identification of very long impulse responses. It provides a perfect parallel decomposition in the transform domain and yields alias free spectral estimates. Its speed of convergence however is limited by a need for excitation at points spaced uniformly over the entire frequency axis. This paper proposes to generalize PPS based on some a priori knowledge of the spectral distribution of the signal. Using rotations and dilations PPS can zoom in on the spectral range of interest and provide good estimates at a fast rate. Finally, we present a generalized form for sub-band decomposition of multirate systems, which would form an ideal platform for developing parallel algorithms in the frequency domain.