An algorithm for matrix extension and wavelet construction |
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| Authors: | W Lawton S L Lee Zuowei Shen |
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| Institution: | Institute of Systems Science, National University of Singapore, Heng Mui Keng Terrace, Kent Ridge, Singapore 0511 ; Department of Mathematics, National University of Singapore, 10 Kent Ridge Crescent, Singapore 0511 ; Department of Mathematics, National University of Singapore, 10 Kent Ridge Crescent, Singapore 0511 |
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| Abstract: | This paper gives a practical method of extending an  matrix  ,  , with Laurent polynomial entries in one complex variable  , to a square matrix also with Laurent polynomial entries. If  has orthonormal columns when  is restricted to the torus  , it can be extended to a paraunitary matrix. If  has rank  for each  , it can be extended to a matrix with nonvanishing determinant on  . The method is easily implemented in the computer. It is applied to the construction of compactly supported wavelets and prewavelets from multiresolutions generated by several univariate scaling functions with an arbitrary dilation parameter. |
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| Keywords: | Wavelets prewavelets matrix extension splines |
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