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.

The 2D separable wavelet transform offers limited directionality because it can only provide three directional subbands. The finer directional wavelet transform has been proposed to improve the directionality of the 2D separable wavelet transform. The finer directional wavelet transform employs quadrant filters on subband outputs of the 2D separable wavelet transform. It divides the three directional subband of wavelet transform into six finer directional subbands. Even though the finer directional wavelet transform has advantages of being non redundant and has efficient separable implementation, it suffers in performance due to aliasing. The aliasing occurs due to the quadrant filters' inherent frequency response characteristics and thus cannot be eliminated. This paper addresses the aliasing involved in the implementation of the finer directional wavelet transform and recommends ways to reduce the aliasing.

It is a well-known fact that (compact-support) dyadic wavelets [based on the two channel filter banks (FBs)] cannot be simultaneously orthogonal and symmetric. Although orthogonal wavelets have the energy preservation property, biorthogonal wavelets are preferred in image processing applications because of their symmetric property. In this paper, a novel method is presented for the design of almost symmetric orthogonal wavelet FB. Orthogonality is structurally imposed by using the unnormalized lattice structure, and this leads to an objective function, which is relatively simple to optimize. The designed filters have good frequency response, flat group delay, almost symmetric filter coefficients, and symmetric wavelet function.