Journal of Fourier Analysis and Applications

, Volume 3, Issue 1, pp 23–41

Smoothing minimally supported frequency wavelets: Part II

  • Eugenio Hernández
  • Xihua Wang
  • Guido Weiss
Article

Abstract

The main purpose of this paper is to give a procedure to “mollify” the low-pass filters of a large number ofMinimally Supported Frequency (MSF) wavelets so that the smoother functions obtained in this way are also low-pass filters for an MRA. Hence, we are able to approximate (in the L2-norm) MSF wavelets by wavelets with any desired degree of smoothness on the Fourier transform side. Although the MSF wavelets we consider are bandlimited, this may not be true for their smooth approximations. This phenomena is related to the invariant cycles under the transformation x ↦2x (mod2π). We also give a characterization of all low-pass filters for MSF wavelets. Throughout the paper new and interesting examples of wavelets are described.

Math Subject Classification

Primary 42C15 

Keywords and Phrases

wavelet multiresolution analysis band-limited invariant cycle 

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Copyright information

© CRC Press LLC 1997

Authors and Affiliations

  • Eugenio Hernández
    • 1
  • Xihua Wang
    • 2
  • Guido Weiss
    • 2
  1. 1.Matemáticas, Universidad Autónoma de MadridMadridSpain
  2. 2.Department of MathematicsWashington UniversitySt. Louis

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