Construction of Algebraic Wavelet Coefficients
Thomas Beth, Andreas Klappenecker, Armin Nückel · 1994
In this paper we discuss a method for construction of algebraic wavelet coefficients, i.e., wavelet coefficients lying in an algebraic extension field of Q: The method relies on a strengthened version of a theorem due to L. FEJÉR and F. RIESZ. As an application, we prove that the Daubechies wavelets have algebraic wavelet coefficients. We show that there exist uncountably many transcendent scaling coefficient sequences. Furthermore, we prove that the set of parameters for algebraic wavelet coefficient sequences (up to a given length) is dense in the parameter space of the Pollen parametrization. Algebraic wavelet coefficient sequences may lead to faster processing units in VLSI implementations of the fast wavelet transform. 1