Multiscale Modeling using Signal Adapted Filter Bank

In this work, we present a multi-scale modelling technique using a signal adapted multirate filter bank. Unlike the existing multi-resolution modelling strategies, the proposed algorithm can be implemented using a signal adaptive, fast, recursive algorithm which is computationally efficient. The analysis filter bank, used in this work is a multivariate whitening filter whose outputs are orthogonal in time as well as across channels. The analysis filter bank whitens the input signal in different spectral bands. The synthesis filter bank, proposed here, has been designed to reconstruct only the given signal and not every energy signal, as is done in the perfect reconstruction filter bank case. Outputs of the M-synthesis filters, thus, provide the required M-orthogonal sub-band constituents of the given signal. Since the proposed modelling scheme is signal dependent it can be efficient used for applications like energy compaction, dimension reduction etc. The performance of the proposed algorithm does not deteriorate for long data and, also, the number of sub-bands is not arbitrary. The efficacy of the algorithm has been verified via simulation studies.