High order balanced multiwavelets

In this paper, we study the issue of regularity for multi-wavelets. We generalize here the concept of balancing for higher degree discrete-time polynomial signals and link it to a very natural factorization of the lowpass refinement mask that is the counterpart of the well-known zeros at pi condition for wavelets. This enables us to clarify the subtle relations between approximation power, smoothness and balancing order. Using these new results, we are also able to construct a family of orthogonal multiwavelets with symmetries and compact support that is indexed by the order of balancing. More details (filters coefficients, drawings of the whole family, frequency responses,...) can be obtained on the [WEB] at http://lcavwww.epfl.ch/similar to lebrun.