A family of orthonormal wavelet bases with dilation factor 4

In this paper, we study a method for the construction of orthonormal wavelet bases with dilation factor 4. More precisely, for any integer M >0, we construct an orthonormal scaling filter mM(ξ ) that generates a mother scaling function φM, associated with the dilation factor 4. The computation of the different coefficients of |mM(ξ )|2 is done by the use of a simple iterative method. Also, this work shows how this construction method provides us with a whole family of compactly supported orthonormal wavelet bases with arbitrary high regularity. A first estimate of α(M), the asymptotic regularity of φM is given by α(M) ∼ 0.25M. Examples are provided to illustrate the results of this work.  2005 Elsevier Inc. All rights reserved