SeMA Journal

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Construction of dual wavelet frame pairs and signal recovery

  • Ali Akbar Arefijamaal
  • Fahimeh Arabyani Neyshaburi
  • Samaneh Matindoost
Article
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Abstract

Signal processing is an enabling technology that helps us to denote any operation which modifies or analyzes the information contained in a signal. In this paper, we first decompose the original signal by a wavelet packet frame and analyze the coefficients. Then, by using dual wavelet frames, we reconstruct the original signal. In this reconstruction, the standard choice for duals which plays a key role is the canonical dual. Our aim is to develop new duals to obtain more accurate results. To this end, we consider wavelet frames which Fourier transform of generators form a partition of unity. Then we introduce several explicit duals for them and compare the advantage of these duals in signal processing. This indicates that we may obtain more reliable estimates by alternate duals.

Keywords

Wavelet frame Dual wavelet frame Partition of unity 

Mathematics Subject Classification

Primary 42C15 Secondary 42C40 

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Copyright information

© Sociedad Española de Matemática Aplicada 2018

Authors and Affiliations

  • Ali Akbar Arefijamaal
    • 1
  • Fahimeh Arabyani Neyshaburi
    • 1
  • Samaneh Matindoost
    • 2
  1. 1.Department of Mathematics and Computer SciencesHakim Sabzevari UniversitySabzevarIran
  2. 2.Department of Electrical EngineeringHakim Sabzevari UniversitySabzevarIran

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