An Algorithm for Matrix Extension and Wavelet Construction 3
نویسنده
چکیده
This paper gives a practical method of extending an nr matrix P (z), r n, with Laurent polynomial entries in one complex variable z, to a square matrix also with Laurent polynomial entries. If P (z) has orthonormal columns when z is restricted to the torus T, it can be extended to a paraunitary matrix. If P (z) has rank r for each z 2 T, it can be extended to a matrix with nonvanishing determinant on T. The method is easily implemented in the computer. It is applied to the construction of compactly supported wavelets and pre-wavelets from multiresolutions generated by several univariate scaling functions with an arbitrary dilation parameter.
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