ARMA Models over Orthonormal Wavelet Subbands

Multi-component signals may be separated according to the subspace in which they reside. System identification of signals in multiresolution subspaces requires an understanding of changes in a general white noise excited ARMA process as it is traversed through critically sampled wavelet filter banks. We show that at sufficiently high scale levels, an ARMA process becomes a special MA process given by the sum of b[k]epsiv_k[n] where b[k] are the numerator coefficients of the full band ARMA process and, epsiv_k[n] are white noise correlated to each other. We propose an algorithm to determine the ARMA coefficients at any desired level