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Circuits, Systems, and Signal Processing

, Volume 37, Issue 8, pp 3295–3312 | Cite as

Design of Time–Frequency-Localized Two-Band Orthogonal Wavelet Filter Banks

  • Dinesh Bhati
  • Ram Bilas Pachori
  • Manish Sharma
  • Vikram M. Gadre
Article

Abstract

In this paper, we design time–frequency-localized two-band orthogonal wavelet filter banks using convex semidefinite programming (SDP). The sum of the time variance and frequency variance of the filter is used to formulate a real symmetric positive definite matrix for joint time–frequency localization of filters. Time–frequency-localized orthogonal low-pass filter with specified length and regularity order is designed. For nonmaximally regular two-band filter banks of length twenty, it is found that, as we increase the regularity order, the solution of the SDP converges to the filters with time–frequency product (TFP) almost same as the Daubechies maximally regular filter of length twenty. Unlike the class of Daubechies maximally regular minimum phase wavelet filter banks, a rank minimization algorithm in a SDP is employed to obtain mixed-phase low-pass filters with TFP of the filters as well as the scaling and wavelet function better than the equivalent two-band Daubechies filter bank.

Keywords

Two-band filter bank Orthogonal wavelet Semidefinite programming Uncertainty principle Time–frequency localization 

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Dinesh Bhati
    • 1
  • Ram Bilas Pachori
    • 2
  • Manish Sharma
    • 3
  • Vikram M. Gadre
    • 4
  1. 1.Department of Electronics EngineeringAcropolis Institute of Technology and ResearchIndoreIndia
  2. 2.Discipline of Electrical EngineeringIndian Institute of Technology IndoreIndoreIndia
  3. 3.Department of Electrical EngineeringInstitute of Infrastructure Technology Research and ManagementAhmadabadIndia
  4. 4.Department of Electrical EngineeringIndian Institute of Technology BombayMumbaiIndia

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