The complete length sixteen parametrized wavelets
David Roach · Sampling Theory Signal Processing and Data Analysis · 2025
Abstract 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.