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 L2( R) is obtained. Analogous results are also derived for deterministic signals. Some illustrative examples and simulations are presented.
Bibliographical noteFunding Information:
Manuscript received April 17, 1992; revised February 10, 1995. This work was supported by the National Science Foundation under Grant NSF-MIP 9210230. The associate editor coordinating the review of this paper and approving it for publication was Dr. Robert A. Gabel. The authors are with the Department of Electrical Engineering, University of Viinia, Chadottesville, VA 22903-2442 USA. IEEE Log Number 9412625.