Matrix parametrization of compactly supported orthonormal wavelets

We derive a new set of necessary and sufficient conditions for the filter coefficients of the two-scale difference equation to yield an orthogonal wavelet of compact support. The conditions constitute a linear set of equations of an arbitrary decision vector of half the filter size. The vector of the filter coefficients is a differentiable function of the decision vector. The formulation enables the optimization of the filter design under any regular objective function. The proposed parametrization is used to design customized orthonormal wavelets and to reproduce the classical orthogonal wavelets as a solution of a nonlinear optimization problem.