THE CHOI-WILLIAMS-ANALYSIS OF NON-LINEAR WAVE PROCESSES

DOI: https://doi.org/10.15407/rpra20.03.223

O. V. Lazorenko, L. F. Chernogor

Abstract


Using the Choi-Williams transform, belonging to the Cohen’s class of non-linear transforms, the time-frequency analysis of the model signals with peculiarities, was made. The models of the Dirac δ-function and its first derivation, their sum with harmonic signal, the limited duration pulse, the sharp changes of amplitude, phase and frequency, the break, the vertical bend, the spire as well as the sum of the spire and the harmonic signalwere studied. The results of сhoi-williams-, wigner- and fourieranalysis were compared. The mentioned transforms were shown to well supplement each other and allow finding more information about time-frequency structure of the signals investigated when they are used together.

Key words: time-frequency analysis, non-linear integral transform, signal with peculiarities

Manuscript submitted 04.06.2015

Radio phys. radio astron. 2015, 20(3): 223-237

REFERENCES

1. POTAPOV, A. A., 2005. Fractals in radiophysics and radar: Sample topology. Moscow, Russia: Universitetskaya kniga Publ. (in Russian).

2. DMITRIEV, A. S., KLETSOV, A. V., LAKTYUSHKIN, A. M., PANAS, A. I. and STARKOV, S. O., 2006. Ultra-wideband wireless communication based on dynamic chaos. Radiotekhnika i Electronika, vol. 51, no. 10, pp. 1193–1209 (in Russian).

3. BOLOTOV, V. N. and TKACH, Y. V., 2008. Fractal communication system. Zhurnal tekhnicheskoy fiziki, vol. 78, no. 9, pp. 91–95 (in Russian).

4. LAZORENKO, O. V. and CHERNOGOR, L. F., 2009. Ultra-wideband signals and processes: Monograph. Kharkiv, Ukraine: V. N. Karazin Kharkiv National University Publ. (in Russian).

5. DMITRIEV, A. S., EFREMOVA, E. V. and PANAS, A. I., 2012. Direct-chaotic wireless communication systems. In A. A. Borisov, ed. Fryazino Electronics School. Moscow, Russia: Yanus-K Publ., pp. 455–475 (in Russian).

6. MATIN, A. A., ed., 2012. Ultra Wideband – Current Status and Future Trends. Rieka, Croatia: InTech DOI: https://doi.org/10.5772/2588

7. THOMA, R., KNOCHEL, R. H., SACHS, J., WILLMS, I. and ZWICK, T., eds. 2013. Ultra-Wideband Radio Technologies for Communications, Localization and Sensor Applications. Rieka, Croatia: InTech DOI: https://doi.org/10.5772/2648

8. COHEN, L., 1995. Time-Frequency Analysis: Theory and Applications. New York, USA: Prentice-Hall Publ.

9. MALLAT, S., 2009. A Wavelet Tour of Signal Processing. The Sparse Way. New York, USA: Academic Press.

10. MADISETTI, V. K., ed. 2010. The Digital Signal Processing Handbook. Boca Raton, USA: CRC Press.

11. BALEANU, D., ed. 2012. Advances in Wavelet Theory and Their Applications in Engineering, Physics and Technology. Rieka, Croatia: InTech.

12. AUGER, F., FLANDRIN, P., GONCALVES, P. and LEMOINE, O., 2005. Time-Frequency Toolbox Reference Guide. – Houston, USA: Rice University.

13. VISHNIVETSKY, O. V., KRAVCHENKO, V. F., LAZORENKO, O. V. and CHERNOGOR, L. F., 2006. Wigner transform and atomic functions in digital signal processing. Electromagnitnye volny i elektronnye sistemy, vol. 11, no. 6, pp. 26–38 (in Russian).

14. CHOI, H.-J. and WILLIAMS, W. J., 1989. Improved Time-Frequency Representation of Multicomponent Signals Using Exponential Kernels. IEEE Trans. Acoust. Speech Signal Process., vol. 37, no. 6, pp. 862–871. DOI: https://doi.org/10.1109/ASSP.1989.28057

15. VISHNIVETSKY, O. V., LAZORENKO, O. V. and CHERNOGOR, L. F., 2008. The Wigner-Analysis of Model Signals with Peculiarities. Radiofizika i radioastronomiya, vol. 13, no. 2, pp. 195–209 (in Russian).

16. VISHNIVETSKY, O. V., LAZORENKO, O. V. and CHERNOGOR,
L. F., 2007. The Choi-Williams Analysis in Digital Signal Processing. Radio Phys. Radio Astron., vol. 12, no. 4, pp. 410–432 (in Russian).

17. VISHNIVETSKY, O. V., LAZORENKO, O. V. and CHERNOGOR,
L. F., 2007. Analysis of Non-Linear Wave Processes Using Wigner Transform. Radio Phys. Radio Astron., vol. 12, no. 3, pp. 295–310 (in Russian).

18. LAZORENKO, O. V., LAZORENKO, S. V. and CHERNOGOR,
L. F., 2007. Wavelet Analysis of the Model Signals with Peculiarities. 1. Continuous Wavelet Transform. Radio Phys. Radio Astron., vol. 12, no. 2, pp. 182–204 (in Russian).

19. LAZORENKO, O. V., LAZORENKO, S. V. and CHERNOGOR,
L. F., 2007. Wavelet Analysis of the Model Signals with Peculiarities. 2. Analytical and Discrete Wavelet Transforms. Radio Phys. Radio Astron., vol. 12, no. 3, pp. 278–294 (in Russian).

20. WIGNER, E. P., 1932. On the quantum correction for thermodynamic equilibrium. Phys. Rev., vol. 40, pp. 749–759. DOI: https://doi.org/10.1103/PhysRev.40.749

21. LAZORENKO, O. V. and CHERNOGOR, L. F., 2007. The System Spectral Analysis: Theoretical Bases and Practical Applications. Radiofizika i radioastronomiya, vol. 12, no. 2, pp. 162–181 (in Russian).

22. DYAKONOV, V. P. and ABRAMENKOVA, I. V., 2002. MATLAB. Signal and image processing. Sankt-Petersburg, Russia: Piter Publ. (in Russian).

23. KRAVCHENKO, V. F., LAZORENKO, O. V., PUSTOVOIT, V. I. and CHERNOGOR, L. F., 2007. Choi-Williams Transform and Atomic Function in Digital Signal Processing. Doklady Physics., vol. 52, no. 4, pp. 207–210. DOI: https://doi.org/10.1134/S102833580704009X

24. LAZORENKO, O. V., LAZORENKO, S. V. and CHERNOGOR, L. F., 2005. Wavelet analysis of the non-linear wave processes. Uspekhi sovremennoy radioelecroniki, no. 10, pp. 3–21 (in Russian).

25. LAZORENKO, O. V., PANASENKO, S. V. and CHERNOGOR, L. F., 2005. Adaptive wavelet transform. Electromagnitnye volny i elektronnye sistemy, vol. 10, no. 10, pp. 39–50 (in Russian).


Keywords


time-frequency analysis; non-linear integral transform; signal with peculiarities

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