Theory and Implementation of Wavelet Analyses in Rational Resolution Decompositions

Abstract

The multiresolution analysis (MRA) developed by Mallat and Meyer and further discussed by Daubechies is a useful tool in the analysis of sampled signals such as images and speech. This thesis develops the theory and implementation of a rational-resolution analysis (RRA) as an extension of the dyadic MRA for arbitrary rational dilation factors. We present a method to calculate families of compactly-supported scaling functions and wavelets based on arbitrary integer dilation factors and provide examples. The perfect- reconstruction properties of the RRA are discussed and it is demonstrated that the compactly-supported scaling functions and wavelets do not yield perfect- reconstruction. However, the approximation-reconstruction is demonstrated and families of basis function which do lead to perfect reconstruction are characterized. Finally, comparisons are made between RRAs and conventional MRAs and illustrated with speech signals.

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Document Details

Document Type
Technical Report
Publication Date
Dec 01, 1992
Accession Number
ADA259040

Entities

People

  • Bruce P. Anderson

Organizations

  • Air Force Institute of Technology

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Algorithms
  • C Programming Language
  • Computer Programming
  • Electrical Engineering
  • Engineering
  • Equations
  • Frequency
  • Frequency Domain
  • Frequency Response
  • Image Processing
  • Information Processing
  • Integrals
  • Pattern Recognition
  • Rational Numbers
  • Signal Processing
  • Test And Evaluation
  • Wavelet Transforms

Readers

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