In this paper, a complete parametrization of the length sixteen wavelets is given for the dilation coefficients of the trigonometric polynomials, \(m(\omega)\) , that satisfy the necessary conditions for orthogonality, that is, \(m(0)=\sqrt{2}\) and \(|m(\omega)|^2+|m(\omega+\pi)|^2=2\) . This parametrization has seven free parameters and has a simple compatibility with the shorter length parametrizations for some specific choices of the free parameters. This construction is a more efficient representation than the work of Schneid and Pittner who were the first to give a general technique for the construction of any finite length orthogonal wavelet parametrization in [Schneid, Computing 51, 1993]. These wavelets have varying numbers of vanishing moments and regularity, and continuously transform from one to the other with the perturbation of the free parameters.
