Efficient generation of 1/fβ noise using signal modeling techniques

IEEE Transactions on Circuits and Systems I: Regular Papers

Volumn 55, Issue 6, 2008, Pages 1704-1710

  Ferdi, Youcef ^a   Taleb Ahmed, Abdelmalik ^b,c   Lakehal, Mohamed Reda ^a  

^a UNIVERSITY OF SKIKDA   (Algeria)

^b UNIVERSITÉ DU LITTORAL CÔTE D OPALE   (France)

^c UNIVERSITÉ DE VALENCIENNES   (France)

Author keywords

1 f noise; Al Alaoui's rule; Fractional order integrator (FOI); Power series expansion; Prony's method; Shanks' method; Signal modeling

Indexed keywords

IMPULSE RESPONSE; NUMERICAL METHODS; RATIONAL FUNCTIONS; WHITE NOISE;

1/F NOISE; FRACTIONAL-ORDER INTEGRATOR; POWER SERIES EXPANSIONS; PRONY'S METHOD; SHANKS' METHOD; SIGNAL MODELING;

TRANSFER FUNCTIONS;

EID: 53849115373     PISSN: 10577122     EISSN: None     Source Type: Journal    
DOI: 10.1109/TCSI.2008.918173     Document Type: Article

References (25)

1. M. S. Keshner, "1/f noise," Proc. IEEE, vol. 70, no. 3, pp. 212-218, Mar. 1982.
2. G. W. Wornell, "Wavelet-based representations for 1/f family of fractal processes," Proc. IEEE, vol. 81, no. 10, pp. 1428-1450, Oct. 1993.
3. J. Mukherjee, P. Robin, and S. Akhtar, "An analytic circuit-based model for white and flicker phase noise in LC oscillators," IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 54, no. 7, pp. 1584-1598, Jul. 2007.
4. P. Maffezzoni, "Frequency-shift induced by colored noise in nonlinear oscillators," IEEE Trans. Circuits Syst. II, Exp. Briefs, vol. 54, no. 10, pp. 887-891, Oct. 2007.
5. 2 phase noise in CMOS parallel LC-tank quadrature oscillators," IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 53, no. 8, pp. 1749-1760, Aug. 2006.
6. α power law noise generation," Proc. IEEE vol. 83, no. 5, pp. 802-827, May 1995.
7. J. A. Barnes and D. W. Allan, "A statistical model of flicker noise," Proc. IEEE, vol. 54, no. 2, pp. 176-178, 1966.
8. B. B. Mandelbrot and H. W. Van Ness, "Fractional Brownian motions, fractional noises and applications," SIAM Rev., vol. 10, no. 4, pp. 422-436, 1968.
9. A. V. Chechkin and V. Y. Gonchar, "Fractional Brownian motion based on fractional integration of a white noise," Chaos, Solitons, Fractals vol. 12, pp. 391-398, 2001.
10. M. D. Restituto, A. R. Vásquez, S. Espejo, and J. L. Huertas, "A chaotic switched-capacitor circuit for 1/f noise generation," IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 39, no. 4, pp. 325-328, Apr. 1992.
11. K. Murao, T. Kohda, and M. Yanase, " 1/f noise generator using logarithmic and antilogarithmic amplifiers," IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 39, no. 10, pp. 851-853, Oct. 1992.
12. Y. Q. Chen, B. M. Vinagre, and I. Podlubny, "Continued fraction expansion approaches to discretizing fractional order derivatives-an expository review," Nonlinear Dyn., vol. 38, no. 1-2, pp. 155-170, 2004.
13. M. D. Ortigueira and A. G. Batista, "A fractional linear system view of the fractional Brownian motion," Nonlinear Dyn., vol. 38, no. 1-2, pp. 295-303, 2004.
14. S. Lee, W. Zhao, R. Narasimha, and R. M. Rao, "Discrete-time models for statistically self-similar signals," IEEE Trans. Signal Process., vol. 51, no. 5, pp. 1221-1230, May 2003.
15. Y. Ferdi, "Computation of fractional order derivative and integral via power series expansion and signal modeling," Nonlinear Dyn., vol. 46, no. 1-2, pp. 1-15, 2006.
16. γ power spectrum noise sequence generator," IEEE Trans. Instrum. Meas., vol. 37, no. 4, pp. 615-619, Dec. 1988.
17. C. W. J. Granger and R. Joyeux, "An introduction to long-memory time series models and fractional differencing," J. Time Ser. Anal., vol. 1, no. 1, pp. 15-29, 1980.
18. J. R. M. Hosking, "Fractional differencing," Biometrika, vol. 68, no. 1, pp. 165-176, 1981.
19. M. Deriche and A. H. Tewfik, "Signal modeling with filtered discrete fractional noise processes," IEEE Trans. Signal Process., vol. 41, no. 9, pp. 2839-2849, 1993.
20. C. C. Tseng, S. C. Pei, and S. C. Hsia, "Computation of fractional derivatives using Fourier transform and digital FIR differentiator," Signal Process., vol. 80, no. 1, pp. 151-159, 2000.
21. M. A. Al-Alaoui, "Novel digital integrator and differentiator," Electron. Lett., vol. 29, no. 4, pp. 376-378, 1993.
22. F. Brophy and A. C. Salazar, "Considerations of the Padé approximant technique in the synthesis of recursive digital filters," IEEE Trans. Audio Electroacoust., vol. AE-21, no. 6, pp. 500-505, Dec. 1973.
23. J. L. Shanks, "Recursion filters for digital processing," Geophys. vol. 32, no. 1, pp. 33-51, 1967.
24. Y. Ferdi and B. Boucheham, "Recursive filter approximation of digital fractional differentiator and integrator based on Prony's method," in Proc. ENSEIRB 1st IFAC Workshop Fractional Different. Its Appl., Bordeaux, France, Jul. 19-21, 2004.
25. K. Steiglitz and L. E. McBride, "A technique for the identification of linear systems," IEEE Trans. Autom. Control, vol. AC-10, no. 4, pp. 461-464, Oct. 1965.