Discrete-time models for statistically self-similar signals

IEEE Transactions on Signal Processing

Volumn 51, Issue 5, 2003, Pages 1221-1230

  Lee, Seungsin ^a   Zhao, Wei ^b   Narasimha, Rajesh ^c   Rao, Raghuveer M ^d  

^a ROCHESTER INSTITUTE OF TECHNOLOGY   (United States)

^b KLA TENCOR CORPORATION   (United States)

^c GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

^d Rochester Institute of Technology   (United States)

Author keywords

Communication system traffic; Fractional order models; Long range dependence; Self similarity

Indexed keywords

COMMUNICATION SYSTEMS; COMPUTER SIMULATION; GAUSSIAN NOISE (ELECTRONIC); MATHEMATICAL MODELS; STATISTICS; TELECOMMUNICATION TRAFFIC; TRANSFER FUNCTIONS;

COMMUNICATION SYSTEM TRAFFIC; DISCRETE-TIME MODELS; FRACTIONAL ORDER MODELS; LONG-RANGE DEPENDENCE; STATISTICALLY SELF-SIMILAR SIGNALS;

SIGNAL PROCESSING;

EID: 0012452833     PISSN: 1053587X     EISSN: None     Source Type: Journal    
DOI: 10.1109/TSP.2003.810281     Document Type: Article

References (29)

1. P. Flandrin, "On the spectrum of fractional Brownian motion," IEEE Trans. Inform. Theory, vol. 35, pp. 197-199, Jan. 1989.
2. B. B. Mandelbrot and J. W. Van Ness, "Fractional Brownian motions, fractional noises and applications," SIAM Rev., vol. 10, pp. 422-437, 1968.
3. J. Ramanathan and O. Zeitouni, "On the wavelet transform of fractional Brownian motion," IEEE Trans. Inform. Theory, vol. 37, pp. 1156-1158, July 1991.
4. R. J. Barton and H. V. Poor, "Signal detection in fractional Gaussian noise," IEEE Trans. Inform. Theory, vol. 34, pp. 943-959, Sept. 1988.
5. B. B. Mandelbrot, "Computer experiments with fractional Gaussian noise," Water Resources Res., vol. 5, 1969.
6. α power law noise generation," Proc. IEEE, vol. 83, pp. 802-827, May 1995.
7. M. S. Keshner, "1/f noise," Proc. IEEE, vol. 70, pp. 212-218, 1982.
8. B. B. Mandelbrot, "Some noises with 1/f spectrum, a bridge between direct current and white noise," IEEE Trans. Inform. Theory, vol. IT-13, pp. 289-298, 1967.
9. R. F. Voss, "1/f (flicker) noise: A brief review," in Proc. 33rd Annu. Symp. Frequency Contr., 1979, pp. 40-46.
10. W. E. Leland, M. S. Taqqu, W. Willinger, and D. V. Wilson, "On the self-similar nature of ethernet traffic (extended version)," IEEE/ACM Trans. Networking, vol. 2, pp. 1-15, 1994.
11. K. Park and W. Willinger, Self-Similar Network Traffic and Performance Evaluation. New York: Wiley, 2000.
12. A. Van der Ziel, "On the noise spectra of semi-conductor noise and of flicker effect," Physica, vol. 16, pp. 359-372, 1950.
13. Y. Degerli, F. Lavernhe, P. Magnan, and J. Farre, "Non-stationary noise responses of some fully differential on-chip readout circuits suitable for CMOS image sensors," IEEE Trans. Circuits Syst. II, vol. 46, pp. 1461-1474, Nov. 1999.
14. F. Lavernhe and J. Solhusvik, "Fractional noises: Diffusive model for CCD imager band-pass acquisition chain," in ESAIM: Proc., 1998, pp. 119-130.
15. B. Dubrulle, F. Graner, and D. Sornette, Scale Invariance and Beyond. Berlin, Germany: Springer, 1997.
16. D. R. Cox, "Long-range dependence: A review," in Statistics: An Appraisal, H. A. David and H. T. David, Eds. Ames, IA: Iowa State Univ. Press, 1984, pp. 55-74.
17. J. R. M. Hosking, "Fractional differencing," Biometrika, vol. 68, pp. 165-176, 1981.
18. V. Paxson, "Fast, approximate synthesis of fractional Gaussian noise for generating self-similar network traffic," Comput. Commun. Rev., vol. 27, pp. 5-18, 1997.
19. G. W. Wornell, Signal Processing With Fractals, A Wavelet-Based Approach. Upper Saddle River, NJ: Prentice-Hall, 1996.
20. B. Yazici and R. L. Kashyap, "A class of second-order stationary self-similar processes for 1/f phenomena," IEEE Trans. Signal Processing, vol. 45, pp. 396-410, Feb. 1997.
21. G. W. Wornell and A. V. Oppenheim, "Wavelet-based representations for a class of self-similar signals with application to fractal modulation," IEEE Trans. Inform. Theory, vol. 38, pp. 785-800, Mar. 1992.
22. J. Lamperti, "Semi-stable stochastic processes," Trans. Amer. Math. Soc., vol. 104, pp. 62-78, 1962.
23. J. Beran, Statistics for Long-Memory Processes. New York: Chapman & Hall, 1994.
24. B. Tsybakov and N. D. Georganas, "Self-similar processes in communications networks," IEEE Trans. Inform. Theory, vol. 44, pp. 1713-1725, Sept. 1998.
25. W. Zhao, "Discrete-time continuous-dilation construction of linear scale-invariant systems and multi-dimensional self-similar signals," Ph.D. dissertation, Imag. Sci., Rochester Inst. Technol., Rochester, NY, 1999.
26. A. Papoulis, Probability, Random Variables, and Stochastic Processes, 3rd ed. New York: McGraw-Hill, 1991.
27. D. G. Manolakis, V. K. Ingle, and S. M. Kogon, Statistical and Adaptive Signal Processing: Spectral Estimation, Signal Modeling, Adaptive Filtering, and Array Processing. Boston, MA: McGraw-Hill, 2000.
28. M. S. Taqqu, V. Teverovsky, and W. Willinger, "Estimators for long-range dependence: An empirical study," Fractals, vol. 3, pp. 785-798, 1995.
29. J. D. Gaskill, Linear Systems, Fourier Transforms, and Optics. New York: Wiley, 1978.