I am rather new to the polyphase structure and thought I had understood, but apparently I havent.
My question is I guess very simple: what is the commutator at the input of a polyphase decimator? Is it a memory-less switch or doe it have memory at each phase output of the commutator.
More explicitly: assuming I have a polyphase decomposition of 2 phases. So that I have the P0(z) and P1(z). Assume we are at time t=0 so that the commutator is at position 0 and at this time the input of P0(z) is some value x. Between t=0 and t=1, P0(z) should be computed. at time t=1 the commutator switched and P1(z) (x as input) should compute between t=1 and t=2. So here is where I am not understanding. Between t=1 and t=2 what happens to the INPUT to P0(z)? Is it 0 (as in the commutator is a simple switch without memory) or is the the previous value seen at t=0 (i.e. x).