Skip to main content

Hardware realization of the robust time–frequency distributions


A hardware realization of the L-estimate forms of robust time–frequency distributions is proposed. This hardware realization can be used for instantaneous frequency estimation for signals corrupted by a mixture of impulse and Gaussian noise. The most complex part in the hardware implementation is the block that performs sorting operation. In addition to the continuous realization, a recursive realization of the Bitonic sort network is proposed as well. The recursive approach also provides a fast sorting operation with a significantly reduced number of components. In order to verify the results, the FPGA implementations of the proposed systems were designed.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10


  1. Katkovnik V (1998) Robust M-periodogram. IEEE Trans Signal Process 46(11):3104–3109

    Article  Google Scholar 

  2. Djurović I, Stanković LJ (2001) Robust Wigner distribution with application to the instantaneous frequency estimation. IEEE Trans Signal Process 49(12):2985–2993

    Article  Google Scholar 

  3. Djurović I, Katkovnik V, Stanković LJ (2001) Median filter based realizations of the robust time-frequency distributions. Signal Process 81(7):1771–1776

    Article  MATH  Google Scholar 

  4. Katkovnik V, Djurović I, Stankovic LJ (2000) Instantaneous frequency estimation using robust spectrogram with varying window length. Int J Electron Commun AEU 54(4):193–202

    Google Scholar 

  5. Djurović I, Stanković LJ, Böhme JF (2003) Robust L-estimation based forms of signal transforms and time-frequency representations. IEEE TransSignal Process 51(7):1753–1761

    Article  MathSciNet  Google Scholar 

  6. Djurović I, Stanković LJ, Barkat B (2005) Robust time-frequency distributions based on the robust short time Fourier transform. Ann Telecommun 60(5–6):681–697

    Google Scholar 

  7. Liu KJR (1993) Novel parallel architecture for short-time Fourier transform. IEEE Trans Circ Syst-II 40(12):786–789

    Article  Google Scholar 

  8. Amin MG, Feng KD (1995) Short time Fourier transform using cascade filter structures. IEEE TransCirc Syst 42:631–641

    Article  Google Scholar 

  9. Stanković S, Stanković LJ (1997) An architecture for the realization of a system for time-frequency analysis. IEEE Trans Circ Syst-II 44(7):600–604

    Article  MATH  Google Scholar 

  10. Boashash B, Black JB (1987) An efficient real time implementation of the Wigner-Ville distribution. IEEE TransAcoust Speech Signal Proc 35(11):1611–1618

    Article  Google Scholar 

  11. Stanković S, Stanković LJ, Ivanović V, Stojanović R (2002) An architecture for the VLSI design of systems for time-frequency analysis and time-varying filtering. Ann Telecommun 57(9/10):974–995

    Google Scholar 

  12. Petranovic D, Stankovic S, Stankovic LJ (1997) Special purpose hardware for time frequency analysis. Electron Lett 33(6):464–466

    Article  Google Scholar 

  13. Žarić N, Orović I, Stanković S (2010) Hardware realization of generalized time-frequency distribution with complex-lag argument. EURASIP J Adv Signal Process 2010(879874):10

    Google Scholar 

  14. Batcher K (1968) Sorting networks and their applications. Proc AFIPS Spring Joint Comput Conf 32:307–314

    Google Scholar 

  15. JaJa J (1992) An introduction to parallel algorithms. Addison-Wesley, Reading Massachusetts

    MATH  Google Scholar 

  16. Kumar V, Grama A, Gupta A, Karypis G (1994) Introduction to parallel computing. Benjamin Cummings, Redwood City

    MATH  Google Scholar 

  17. Knuth DE (1973) The art of computer programming, vol 3. Addison Wesley, Reading

    Google Scholar 

  18. Culler DE, Dusseau A, Martin R, Schauser KE (1994) Fast parallel sorting under LogP: from Theory and Practice. In: Hey T, Ferante J (eds) Portability and Performance of Parallel Programming. Wiley

  19. Florin M, Schauser KE (1997) Optimizing parallel bitonic sort. 11th International Parallel Processing Symposium (IPPS ‘97), Geneva, Switzerland, pp 303–309

  20. Mueller R, Teubner J, Alonso G (2009) Data Processing on FPGAs. Proc. of the 35th Int'l Conference on Very Large Data Bases (VLDB)/ Proc. of the VLDB Endowment, vol 2, Lyon, France

  21. Harkins J, El-Ghazawi T, El-Araby E, Huang M (2005) Performance of Sorting Algorithms on the SRC 6 Reconfigurable Computer. IEEE International Conference On Field-Programmable Technology (FPT 2005), Singapore, pp 295–296

  22. Zhu J, Sutton P (2003) An FPGA implementation of Kak's instantaneously-trained, Fast-Classification neural networks. In: Proc of IEEE International Conference on Field-Programmable Technology (FPT), Tokyo, Japan, pp 126–133

  23. Stanković LJ (1994) A method for time-frequency analysis. IEEE Trans Signal Process 42(1):225–229

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations


Corresponding author

Correspondence to Nikola Žarić.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Žarić, N., Stanković, S. & Uskoković, Z. Hardware realization of the robust time–frequency distributions. Ann. Telecommun. 69, 309–320 (2014).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:


  • Robust time–frequency distributions
  • Bitonic sort network
  • FPGA implementation