Multi-wavelets from B-spline super-functions with approximation order

  • Authors:

  • Hüseyin Özkaramanli;Asim Bhatti;Bulent Bilgehan

  • Affiliations:

  • Electrical and Electronics Engineering Department, Eastern Mediterranean University, Magosa, Mersin 10, Turkey;Electrical and Electronics Engineering Department, Eastern Mediterranean University, Magosa, Mersin 10, Turkey;Electrical and Electronics Engineering Department, Eastern Mediterranean University, Magosa, Mersin 10, Turkey

  • Venue:
  • Signal Processing
  • Year:
  • 2002

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Abstract

Approximation order is an important feature of all wavelets. It implies that polynomials up to degree p - 1 are in the space spanned by the scaling function(s). In the scalar case, the scalar sum rules determine the approximation order or the left eigenvectors of the infinite down-sampled convolution matrix H determine the combinations of scaling functions required to produce the desired polynomial. For multi-wavelets the condition for approximation order is similar to the conditions in the scalar case. Generalized left eigenvectors of the matrix Hf; a finite portion of H determines the combinations of scaling functions that produce the desired superfunction from which polynomials of desired degree can be reproduced. The superfunctions in this work are taken to be B-splines. However, any refinable function can serve as the superfunction. The condition of approximation order is derived and new, symmetric, compactly supported and orthogonal multi-wavelets with approximation orders one, two, three and four are constructed.