Solving the Saint-Venant equations by numerical methods like finite element and finite difference methods yields an unstable solution for a fairly large open channel. Multiple Knot B-Spline Wavelets (MKBSW) are in the class of semi-orthogonal wavelets that have compact support. Hence, these basis functions are suitable for solving the Saint-Venant equations. However, solving the Saint-Venant eq...

The Wavelet Transform generates a sparse multi-scale signal representation which may be readily compressed. To implement such a scheme in hardware, one must have a computationally cheap method of computing the necessary transform data. The use of semi-orthogonal quadratic spline wavelets allows one to maintain a suitable level of smoothness in the MRA whilst enabling cheap computation. Among th...

The Wavelet Element Method (WEM) provides a construction of multiresolution systems and biorthogonal wavelets on fairly general domains. These are split into subdomains that are mapped to a single reference hypercube. Tensor products of scaling functions and wavelets defined on the unit interval are used on the reference domain. By introducing appropriate matching conditions across the interele...

This paper is to construct tight wavelet frame systems containing a set of canonical filters by applying the unitary extension principle of [20]. A set of filters are canonical if the filters in this set are generated by flipping, adding a conjugation with a proper sign adjusting from one filter. The simplest way to construct wavelets of s-variables is to use the 2−1 canonical filters generated...

This paper investigates the mathematical background of multiresolution analysis in the specific context where the signal is represented by irregularly sampled data at known locations. The study is related to the construction of nested piecewise polynomial multiresolution spaces represented by their corresponding orthonormal bases. Using simple spline basis orthonormalization procedures involves...