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It is very important for generating an orthonormal multiwavelet system to construct a conjugate quadrature filter (CQF). In this paper, a general method of deriving a length-J + 1 conjugate quadrature filter with multiplicity r and scale a from a length-J conjugate quadrature filter is obtained. As a special case, we study generally the construction of a length-J + 1 conjugate quadrature filter which...
This paper examines a class of univariate wavelet functions with a matrix factorization. Firstly, the property of an important function is surveyed. Secondly, the result is applied to demonstrate the properties of the filters as well as the scaling and wavelet functions. It is presented that two scaling functions are reflections of each other for some pair of parameters. Examples are developed to...
This paper presents a novel approach for constructing symmetric compactly supported biorthogonal multiwavelets with short sequences. Starting from the symmetric properties of scaling and wavelet functions, parameterized symmetric forms of the polyphase matrices can be derived, which greatly simplify the construction problem of compactly supported biorthogonal multiwavelets. Moreover, according to...
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