Nearly symmetric orthogonal wavelets with non-integer DC group delay

This paper investigates the design of Coiflet-like nearly symmetric compactly supported orthogonal wavelets. The group delay is used as the main vehicle by which near symmetry is achieved. By requiring a specified degree of flatness of the group delay at ω = 0 (equivalent to appropriate moment conditions), near symmetry is achieved. Grobner bases are used to obtain the solutions to the defining nonlinear equations. It is found that the DC group delay that maximizes the group delay flatness at ω = 0 is irrational - and for a length 10 orthogonal wavelet with three vanishing moments, the solution is presented.