Characterization of orthonormal high-order balanced multiwavelets in terms of moments
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In this paper, we derive a characterization of orthonormal balanced multiwavelets of order p in terms of the continuous moments of the multiscaling function Φ. As a result, the continuous moments satisfy the discrete polynomial preserving properties of order p (or degree p-1) for orthonormal balanced multiwavelets. We derive polynomial reproduction formula of degree p-1 in terms of continuous moments for orthonormal balanced multiwavelets of order p. Balancing of order p implies that the series of scaling functions with the discrete-time monomials as expansion coefficients is a polynomial of degree p-1. We derive an algorithm for computing the polynomial of degree p-1.
Abstract
In this paper, we derive a characterization of orthonormal balanced multiwavelets of order p in terms of the continuous moments of the multiscaling function Φ. As a result, the continuous moments satisfy the discrete polynomial preserving properties of order p (or degree p-1) for orthonormal balanced multiwavelets. We derive polynomial reproduction formula of degree p-1 in terms of continuous moments for orthonormal balanced multiwavelets of order p. Balancing of order p implies that the series of scaling functions with the discrete-time monomials as expansion coefficients is a polynomial of degree p-1. We derive an algorithm for computing the polynomial of degree p-1.
참고문헌 (11)
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