Signal Modeling Using Transmultiplexer Structures

This article presents signal modeling techniques by using different transmultiplexer structures. By this methodology any arbitrary signal x(n) isinl2 can be reconstructed as an output of an FIR filter C(z) of an order L. This filter is excited by a signal y(n)= Sigma _i=0 ^M-1 Sigma_k=-infin S_i(k) f_i (n_kM) isinl², which can be considered as an output of the left hand side of the transmultiplexer structure. Where, f_i(n) is the impulse response of the filter Fi(z) which is oversampled by M>L. The inputs to the filters Fi(z) are si(n) and their approximation can be obtained as: Scirc(n)= Sigma_k=-infin ^infin x(k)h_i (Mn - k) isinl2 , i=0,..., M - 1, where h_i(n) is the impulse response of the filter Hi (z) which is decimated by M. The signals scirci(n), i = 0,...,M -1 can be considered as an output of the right hand side of the transmultiplexer structure. By this proposed methodology, the signal modeling is equivalent to finding the set of filters Hi(z) and Fi(z) for a given signal x(n) isinl2 and for a given FIR filter C(z) such that si(n) ap scirci(n), i= 0,...,M -1.