Compactly supported orthogonal wavelets have found wide application in prac
tice. A disadvantage of these wavelets is that they are not symmetric. Thus
they do not have a linear phase, which is a property often desired in some
applications such as signal processing. In this paper, degrees of freedom
are introduced in the design to minimize the asymmetry of the wavelets. The
results indicate that compactly supported orthogonal wavelets designed via
optimization are much less asymmetric and have an approximately linear pha
se.