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Synthesis of an Optimal Wavelet Based on Auditory Perception Criterion

Abstract

A method is proposed for synthesizing an optimal wavelet based on auditory perception criterion for dyadic filter bank implementation. The design method of this perceptually optimized wavelet is based on the critical band (CB) structure and the temporal resolution of human auditory system (HAS). The construction of this compactly supported wavelet is done by designing the corresponding optimal FIR quadrature mirror filter (QMF). At first, the wavelet packet (WP) tree is obtained that matches optimally with the CB structure of HAS. The error in passband energy of the CB channel filters is minimized with respect to the ideal QMF. The optimization problem is formulated in the lattice QMF domain and solved using bounded value global optimization technique. The corresponding wavelet is obtained using the cascade algorithm with the support being decided by the temporal resolution of HAS. The synthesized wavelet is maximally frequency selective in the critical bands with temporal resolution closely matching with that of the human ear. The design procedure is illustrated with examples, and the performance of the synthesized wavelet is analyzed.

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Correspondence to Abhijit Karmakar.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Keywords

  • Global Optimization
  • Temporal Resolution
  • Quantum Information
  • Design Procedure
  • Filter Bank