Ten lectures on wavelets
Fractal functions and wavelet expansions based on several scaling functions
Journal of Approximation Theory
A study of orthonormal multi-wavelets
Applied Numerical Mathematics - Special issue on selected keynote papers presented at 14th IMACS World Congress, Atlanta, NJ, July 1994
An algorithm for matrix extension and wavelet construction
Mathematics of Computation
From wavelets to multiwavelets
Proceedings of the international conference on Mathematical methods for curves and surfaces II Lillehammer, 1997
Symmetric Paraunitary Matrix Extension and Parametrization of Symmetric Orthogonal Multifilter Banks
SIAM Journal on Matrix Analysis and Applications
Hi-index | 7.29 |
Polyphase matrix extension of multiscaling vectors is a fundamental approach for the construction of compactly supported biorthogonal multiwavelets. In this paper, canonical form of polyphase matrices of multiscaling vectors and some properties of solutions satisfying the matrix equation of PR condition are studied through unimodular groups over the Laurent polynomial ring. Under the canonical form of polyphase matrices of multiscaling vectors with the same symmetric center and different symmetric centers, explicit symmetric extension formulas expressed by the polyphase matrices of multiscaling vectors can be obtained. As a result, a novel approach for the construction of symmetric compactly supported biorthogonal multiwavelets with multiplicity 2 is proposed. Finally, several examples are given for verification of our proposed approach.