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The construction and properties of interval multi-wavelets based on symmetric/anti-symmetric orthogonal multi-wavelets on L2(R) with arbitrary supports and multiplicity 2 are introduced. The main contributions include that (1) we study the construction of general orthogonal interval multi-wavelets which preserve the polynomial- reproduction order, and obtain the parametric expressions of interval multi-wavelets; (2) we obtain the decomposition and reconstruction formulas of interval multi-wavelets; (3) we define the “balancing” concept of interval multi-wavelets for the first time and study the construction of orthogonal balancing multi-wavelets, which have been ignored in the past; (4) we study the necessary and sufficient conditions about the symmetry of interval multi-wavelets.
The construction and properties of interval multi-wavelets based on symmetric / anti-symmetric orthogonal multi-wavelets on L2 (R) with arbitrary supports and multiplicity 2 are introduced. The main contributions include (1) we study the construction of general orthogonal interval multi-wavelets which preserve the polynomial-reproduction order, and obtain the parametric expressions of interval multi-wavelets; (2) we obtain the decomposition and reconstruction formulas of interval multi-wavelets; (3) we define the “balancing” concept of interval multi-wavelets for the first time and study the construction of orthogonal balancing multi-wavelets, which have been ignored in the past; (4) we study the necessary and sufficient conditions about the symmetry of interval multi-wavelets.