High Quality Content by WIKIPEDIA articles! An orthogonal wavelet is a wavelet where the associated wavelet transform is orthogonal. That is the inverse wavelet transform is the adjoint of the wavelet transform. If this condition is weakened you may end up with biorthogonal wavelets.A necessary condition for the existence of a solution to the refinement equation is that some power (1+Z)A, A>0, divides the polynomial a(Z):=a_0+a_1Z+dots+a_{N-1}Z^{N-1} (see Z-transform). The maximally possible power A is called polynomial approximation order (or pol. app. power) or number of vanishing moments. It describes the ability to represent polynomials up to degree A-1 with linear combinations of integer translates of the scaling function.

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