Orthonormal bases of compactly supported wavelets II: variations on a theme
SIAM Journal on Mathematical Analysis
An introduction to wavelets
Multirate systems and filter banks
Multirate systems and filter banks
An algorithm for matrix extension and wavelet construction
Mathematics of Computation
Approximation properties of multivariate wavelets
Mathematics of Computation
Approximation properties and construction of Hermite interpolants and biorthogonal mutliwavelets
Journal of Approximation Theory
Vector cascade algorithms and refinable function vectors in Sobolev spaces
Journal of Approximation Theory
Multivariate refinable functions, differences and ideals - a simple tutorial
Journal of Computational and Applied Mathematics
Applications of complex valued wavelet transforms to subbanddecomposition
IEEE Transactions on Signal Processing
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In this paper we study symmetric orthogonal filters with linear-phase moments, which are of interest in wavelet analysis and its applications. We investigate relations and connections among the linear-phase moments, sum rules, and symmetry of an orthogonal filter. As one of the results, we show that if a real-valued orthogonal filter a is symmetric about a point, then a has sum rules of order m if and only if it has linear-phase moments of order 2m. These connections among the linear-phase moments, sum rules, and symmetry help us to reduce the computational complexity of constructing symmetric real-valued orthogonal filters, and to understand better symmetric complex-valued orthogonal filters with linear-phase moments. To illustrate the results in the paper, we provide many examples of univariate symmetric orthogonal filters with linear-phase moments. In particular, we obtain an example of symmetric real-valued 4-orthogonal filters whose associated orthogonal 4-refinable function lies in C^2(R).