Skip to main content

Construction of optimal algorithms for mass computations in digital filtering problems

Abstract

Theoretical results are reviewed that are concerned with the construction of speed-optimal parallel-pipeline algorithms for mass calculations in solving filtering problems. The optimality is proved in the corresponding classes of algorithms equivalent in terms of information graphs. The effectiveness of using the developed algorithmic constructions for filtering problems is investigated.

This is a preview of subscription content, access via your institution.

References

  1. 1.

    L. P. Yaroslavskii, Digital Signal Processing in Optics and Holography: Introduction to Digital Optics [in Russian], Radio i Svyaz’, Moscow (1987).

    Google Scholar 

  2. 2.

    V. K. Zadiraka and S. S. Melnikova, Digital Signal Processing [in Russian], Naukova Dumka, Kiev (1993).

    Google Scholar 

  3. 3.

    M. M. Jacymirski, Fast Algorithms of Orthogonal Trigonometrical Transformations [in Ukranian], Akademichnyi Ekspres, L’viv (1997).

    Google Scholar 

  4. 4.

    O. V. Timchenko, Difference Methods of Digital Filtering [in Ukrainian], Fenix, L’viv (1999).

    Google Scholar 

  5. 5.

    L. Lamport, “The parallel execution of DO loops,” Comm. ACM, 17, No. 2, 83–93.

  6. 6.

    A. N. Svenson (ed.), Parallel Information Processing: Parallel Methods and Tools of Pattern Recognition [in Russian], Vol. 2, Naukova Dumka, Kiev (1985).

    Google Scholar 

  7. 7.

    A. V. Lyulyakov, “Construction of a dense schedule for a conveyor computing system during digital filtering of a signal,” in: Theoretical Problems of Information Processing Systems, VTs SO AN SSSR, Novosibirsk (1986), pp. 72–85.

    Google Scholar 

  8. 8.

    V. S. Markhivka and M. M. Jacymirski, “Parallelization of programs of fast orthogonal transformations in multiprocessor systems,” Visn. Derzh. Un-tu “L’vivs’ka Politekhnika,” Computer Engineering and Information Technologies, No. 349, 21–26 (1998).

  9. 9.

    A. P. Ershov (ed.), Algorithms, Software, and Architecture of Multiprocessor Computing Systems [in Russian], Nauka, Moscow (1982).

    Google Scholar 

  10. 10.

    H. T. Kung and C. E. Leiserson, “Systolic arrays (for VLSI),” in: Proc. Symp. on Sparse Matrix Comput. (Knoxville, 1978), SIAM, Philadelphia (1979), pp. 256–282.

    Google Scholar 

  11. 11.

    T. P. Tishchenko, “Digital filtering on systolic structures,” in: Theory of Programming and Means for Description of Parallelism of Discrete Systems, VTs SO AN SSSR, Novosibirsk (VTs SO AN SSSR, Novosibirsk (1985), pp. 90–103.

    Google Scholar 

  12. 12.

    G. A. Kukharev, A. Yu. Tropchenko, and V. P. Shmerko, Systolic Processors for Signal Processing [in Russian], Belarus, Minsk (1988).

  13. 13.

    Yu. S. Kanevskii, Systolic Processors [in Russian], Tekhnika, Kiev (1991).

    Google Scholar 

  14. 14.

    A. N. Kostyunin, “Application of systolic processors to adaptive signal filtering,” USiM, No. 6, 32–35 (1991).

  15. 15.

    Ya. A. Dubrov (ed.), “A systolic convolution processor,” Prepr. No. 5-91, NTTs “Integral,” L’vov (1991).

    Google Scholar 

  16. 16.

    S. M. Ivanov and A. Yu. Tropchenko, “Conveyor bit-slice rank filtering algorithms and their realization on FPLICs,” in: Proc. 5th Intern. Conf. “Pattern Recognition and Information Processing,” 2, Minsk (1999), pp. 239–243.

    Google Scholar 

  17. 17.

    O. I. Liskevich, R. I. Liskevich, and M. M. Jacymirski, “Algorithmic approach to the construction of neural networks of linear filtering of signals,” in: Proc. Intern. Conf. on Control AVTOMATIKA-2000, L’viv, Sect. 7, Part 1 (2000), pp. 318–323.

  18. 18.

    T. Lee, “Three-dimensional microelectronics,” Open Systems, No. 2 (2002), www.osp.ru/os//2002/02/022.htm.

  19. 19.

    M. S. Yadzhak, “Optimization of systolic computations in solving digital filtering problems,” in: Proc. V. M. Glushkov Cybernetics Institute of NASU on the Theory of Computation, Kyiv (1999), 386–390.

  20. 20.

    M. S. Yadzhak, “Some computing tools of realization of digital filtering algorithms,” Volyn. Mat. Visn., No. 9, 90–99 (2002).

  21. 21.

    M. S. Yadzhak, “Organization of systolic computations during cascade digital filtering,” Volyn. Mat. Visn., Ser. Prikl. Mat., No. 1 (10), 153–160 (2003).

  22. 22.

    V. A. Val’kovskii, “An optimal algorithm for solving the problem of digital filtering,” Pattern Recognition and Image Analysis, 4, No. 3, 241–247 (1994).

    Google Scholar 

  23. 23.

    V. A. Val’kovskii and M. S. Yadzhak, “Simulation and realization of neural networks on models of parallel information processing,” in: Proc. Intern. Conf. “Methods and Tools of Transformation and Processing of Analog Information,” 1, UlGTU, Ulyanovsk (1999), pp. 53–55.

    Google Scholar 

  24. 24.

    V. A. Valkovskii and M. S. Yadzhak, “Optimal algorithm for solving a two-dimensional digital filtering problem,” Probl. Upravlen. Inf., No. 6, 92–102 (1999).

  25. 25.

    M. S. Yadzhak, “An optimal in one class algorithm for solving the three-dimensional digital filtering problem,” Probl. Upravlen. Inf., No. 6, 66–81 (2000).

  26. 26.

    M. S. Yadzhak, “On the optimality of an algorithm for numerical solution of a generalized digital filtering problem,” Volyn. Mat. Visn., No. 7, 181–192 (2000).

  27. 27.

    M. S. Yadzhak, “Numerical realization of cascade digital filtering,” Visn. L’viv. Un-tu, Ser. Prykl. Mat. ta Inf., No. 3, 75–79 (2000).

  28. 28.

    M. S. Yadzhak, “A numerical algorithm for solving a spatial problem of cascade digital filtering,” Probl. Upravl. Inf., No. 3, 107–120 (2004).

  29. 29.

    V. O. Val’kovskii, M. S. Jadzhak, and S. M. Poletayev, “Optimization of quasisystolic computations in solving digital filtering problems,” in: Proc. V. M. Glushkov Cybernetics Institute of NASU on Computer Mathematics and Optimization of Computations, 1, Kyiv (2001), pp. 77–82.

    Google Scholar 

  30. 30.

    M. S. Yadzhak, “Organization of quasisystolic computations during the solution of digital filtering problems,” Visn. L’viv. Un-tu, Ser. Prykl. Mat. Inf., No. 5, 178–183 (2002).

  31. 31.

    M. S. Yadzhak, “Algorithms with bounded parallelism for solving a digital filtering problem,” Probl. Upravlen. Inf., No. 6, 109–118 (2001).

  32. 32.

    M. S. Yadzhak, “Construction of algorithms with bounded parallelism for solving digital filtering problems,” Probl. Upravlen. Inf., No. 6, 92–103 (2002).

  33. 33.

    M. S. Yadzhak, “Realization of algorithms with bounded parallelism for solving a digital filtering problem,” Vidbir I Obrobka Informatsii, No. 25 (101), 103–108 (2006).

  34. 34.

    M. S. Yadzhak, “Simulation of algorithms with bounded parallelism for solving digital filtering problems,” Volyn. Mat. Visn., No. 8, 105–109 (2001).

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to A. V. Anisimov.

Additional information

__________

Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 3–14, July–August 2008.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Anisimov, A.V., Yadzhak, M.S. Construction of optimal algorithms for mass computations in digital filtering problems. Cybern Syst Anal 44, 465–476 (2008). https://doi.org/10.1007/s10559-008-9018-8

Download citation

Keywords

  • optimal parallel-conveyor algorithm
  • digital filtering problem
  • multistage cascade digital filtering
  • quasisystolic structure
  • bounded parallelism
  • algorithm acceleration