RLS design of polyphase components for the interpolation of periodically nonuniformly sampled signals

The generalized sampling theorem states that any analogue signal whose spectrum is limited to 1/T can be exactly recovered from N sequences of samples taken at a rate 2/NT and all having a different sampling phase. When N=2, the exact interpolation formula can be derived quite easily. The ideal interpolation filters have infinite impulse responses. This paper addresses the theoretical question of recovering from the 2 initial sequences, any other sequence taken at the some rate 1/T and with a different sampling phase. FIR filters are derived for a least square interpolation error. Moreover, an adaptive implementation is proposed and formulated as a Kalman algorithm. Simulation results obtained for AR processes show the effectiveness of the solution compared to static solutions