Skip to main content
SpringerLink
Log in

Extraction of Walsh Harmonics by Linear Combinations of Dyadic Shifts

  • Published:
Journal of Mathematical Sciences Aims and scope Submit manuscript

We solve two problems of extracting any term from a signal in the form of a finite sum of the Fourier series with respect to the discrete Walsh functions (in the first case) and the Walsh functions (in the second case) by a linear combination of group shifts of the original signal. We propose a vector version of the discrete time- and frequencythinning wavelet Haar bases, which widely used in encoding and decoding algorithms for the discrete Haar transform. Bibliography: 10 titles.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. V. I. Danchenko and D. Ya. Danchenko, “Extraction of pairs of harmonics from trigonometric polynomials by phase-amplitude operators,” J. Math. Sci., New York 232, No. 3, 322–337 (2018).

    Article  MathSciNet  Google Scholar 

  2. M. S. Bespalov A. S. Golubev, and A. S. Pochenchuk, “Derivation of fast algorithms via binary filtering of signals,” Probl. Inf. Transm. 52, No. 4, 359–372 (2016).

    Article  MathSciNet  Google Scholar 

  3. R. Bellman, Introduction to Matrix Analysis, SIAM, Philadelphia, PA (1997).

    MATH  Google Scholar 

  4. M. S. Bespalov, “Eigenspaces of the discrete Walsh transform” Probl. Inf. Transm. 46, No. 3, 253–271 (2010).

    Article  MathSciNet  Google Scholar 

  5. M. S. Bespalov and V. A. Sklyarenko, Discrete Walsh Functions and Their Applications [in Russian], Valdimir State Univ. Press, Vladimir (2014).

    Google Scholar 

  6. M. S. Bespalov, “On the properties of a new tensor product of matrices” Comput. Math. Math. Phys. 54, No. 4, 561–574 (2014).

    Article  MathSciNet  Google Scholar 

  7. V. N. Malozemov and S. M. Masharskij, “Haar spectra of discrete convolutions,” Comput. Math. Math. Phys. 40, No. 6, 914–921 (2000).

    MathSciNet  MATH  Google Scholar 

  8. V. Yu. Protasov and Yu. A. Farkov, “Dyadic wavelets and refinable functions on a half-line,” Sb. Math. 197, No. 10, 1529–1558 (2006).

    Article  MathSciNet  Google Scholar 

  9. Yu. A. Farkov and S. A. Stroganov, “The use of discrete dyadic wavelets in image processing,” Russ. Math. 55, No. 7, 47–55 (2011).

    Article  Google Scholar 

  10. B. I. Golubov, A. V. Efimov, and V. A. Skvortsov, Walsh Series and Transforms. Theory and Applications, Kluwer Acad., Dordrecht etc. (1991).

    Book  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. A. G. and N. G. Stoletov Vladimir State University, 87, Gor’kogo St, Vladimir, 600000, Russia

    M. S. Bespalov & M. S. Bespalov

Authors
  1. M. S. Bespalov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. S. Bespalov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to M. S. Bespalov or M. S. Bespalov.

Additional information

Translated from Problemy Matematicheskogo Analiza 103, 2020, pp. 21-30.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Bespalov, M.S., Bespalov, M.S. Extraction of Walsh Harmonics by Linear Combinations of Dyadic Shifts. J Math Sci 249, 838–849 (2020). https://doi.org/10.1007/s10958-020-04978-9

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10958-020-04978-9

Search

Navigation