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Computational implementation of the inverse continuous wavelet transform without a requirement of the admissibility condition. / Postnikov, E.B.; Lebedeva, E.A.; Lavrova, A.I.

In: Applied Mathematics and Computation, Vol. 282, 2016, p. 128-136.

Research output: Contribution to journal › Article

Harvard

Postnikov, EB, Lebedeva, EA & Lavrova, AI 2016, 'Computational implementation of the inverse continuous wavelet transform without a requirement of the admissibility condition', Applied Mathematics and Computation, vol. 282, pp. 128-136. https://doi.org/10.1016/j.amc.2016.02.013

APA

Postnikov, E. B., Lebedeva, E. A., & Lavrova, A. I. (2016). Computational implementation of the inverse continuous wavelet transform without a requirement of the admissibility condition. Applied Mathematics and Computation, 282, 128-136. https://doi.org/10.1016/j.amc.2016.02.013

Vancouver

Postnikov EB, Lebedeva EA, Lavrova AI. Computational implementation of the inverse continuous wavelet transform without a requirement of the admissibility condition. Applied Mathematics and Computation. 2016;282:128-136. https://doi.org/10.1016/j.amc.2016.02.013

Author

Postnikov, E.B. ; Lebedeva, E.A. ; Lavrova, A.I. / Computational implementation of the inverse continuous wavelet transform without a requirement of the admissibility condition. In: Applied Mathematics and Computation. 2016 ; Vol. 282. pp. 128-136.

BibTeX

@article{4f4bcc78c62f43aba029283370cae5ba,
title = "Computational implementation of the inverse continuous wavelet transform without a requirement of the admissibility condition",
abstract = "{\textcopyright} 2016 Elsevier Inc. All rights reserved. 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.",
author = "E.B. Postnikov and E.A. Lebedeva and A.I. Lavrova",
year = "2016",
doi = "10.1016/j.amc.2016.02.013",
language = "English",
volume = "282",
pages = "128--136",
journal = "Applied Mathematics and Computation",
issn = "0096-3003",
publisher = "Elsevier",

}

RIS

TY - JOUR

T1 - Computational implementation of the inverse continuous wavelet transform without a requirement of the admissibility condition

AU - Postnikov, E.B.

AU - Lebedeva, E.A.

AU - Lavrova, A.I.

PY - 2016

Y1 - 2016

N2 - © 2016 Elsevier Inc. All rights reserved. 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.

AB - © 2016 Elsevier Inc. All rights reserved. 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.

U2 - 10.1016/j.amc.2016.02.013

DO - 10.1016/j.amc.2016.02.013

M3 - Article

VL - 282

SP - 128

EP - 136

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

SN - 0096-3003

ER -

ID: 7950664