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Computational implementation of the inverse continuous wavelet transform without a requirement of the admissibility condition

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  • Postnikov, Eugene B.
  • Lebedeva, Elena A.
  • Lavrova, Anastasia I.

Abstract

Recently, it has been proven Lebedeva and Postnikov (2014) that the continuous wavelet transform with non-admissible kernels (approximate wavelets) allows an existence of the exact inverse transform. Here, we consider the computational possibility for the realization of this approach. We provide a modified simpler explanation of the reconstruction formula, restricted on the practical case of real valued finite (or periodic/periodized) samples and the standard (restricted) Morlet wavelet as a practically important example of an approximate wavelet. The provided examples of applications include the test function and the non-stationary electro-physical signals arising in the problem of neuroscience.

Suggested Citation

  • Postnikov, Eugene B. & Lebedeva, Elena A. & Lavrova, Anastasia I., 2016. "Computational implementation of the inverse continuous wavelet transform without a requirement of the admissibility condition," Applied Mathematics and Computation, Elsevier, vol. 282(C), pages 128-136.
    • Handle: RePEc:eee:apmaco:v:282:y:2016:i:c:p:128-136
    DOI: 10.1016/j.amc.2016.02.013
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    Cited by:

    1. Tsai-Ning Weng & Ray-Shyan Wu & Tzu-Han Weng & Yi-Ho Chen & Tsai-Chun Lai & Jui-Yun Hsieh & Chu-Chun Hsu & Yuan-Chien Lin, 2025. "Groundwater Level Prediction by Wavelet Deep Learning with Smart Pumping Data," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 39(6), pages 2717-2742, April.
    2. Behera, S. & Saha Ray, S., 2022. "Two-dimensional wavelets scheme for numerical solutions of linear and nonlinear Volterra integro-differential equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 198(C), pages 332-358.
    3. Behera, S. & Ray, S. Saha, 2020. "An operational matrix based scheme for numerical solutions of nonlinear weakly singular partial integro-differential equations," Applied Mathematics and Computation, Elsevier, vol. 367(C).

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