Orthogonal wavelet filters with minimum RMS bandwidth

For a time-limited sequence, the Root-Mean-Square (RMS) bandwidth is the normalized second moment of the spectrum. The RMS bandwidth is a useful and analytically tractable measure of the frequency localization of a discrete-time filter. In this work the design of orthogonal wavelet filter banks with a prescribed number of Vanishing Moment (VM) and having a minimum RMS bandwidth is considered. It is shown that the design problem can be cast as a convex optimization problem for which efficient algorithms and software for its solution exist.