PRINCIPAL COMPONENT FILTER BANKS FOR OPTIMAL MULTIRESOLUTION ANALYSIS

An important issue in multiresolution analysis is that of optimal basis selection. An optimal P-band perfect reconstruction filter bank (PRFB) is derived in this paper, which minimizes the approximation error (in the mean-square sense) between the original signal and its low-resolution version, The resulting PRFB decomposes the input signal into uncorrelated, low-resolution principal components with decreasing variance. Optimality issues are further analyzed in the special case of stationary and cyclostationary processes, By exploiting the connection between discrete-time filter banks and continuous wavelets, an optimal multiresolution decomposition of L(2)(R) is obtained. Analogous results are also derived for deterministic signals, Some illustrative examples and simulations are presented.