Mathematical and Statistical Properties of 1/f (One-Over-F) Noise

see also
mathematical and statistical properties of 1/f2 noise
mathematical studies of long-memory processes

    + 2007

  1. Fabio Principato, Gaetano Ferrante (2007), "1/f Noise decomposition in random telegraph signals using the wavelet transform", Physica A, 380:75-97.

  2. Giovanni Zanella (2007), "Pseudo-periodicity and 1/f noise from the sum of similar intermittent signals", arxiv.org preprint, physics.data-an 0708.3183.
    [abstract]

    + 2006

  3. Ming Li, SC Lim (2006) "A rigorous derivation of power spectrum of fractional Gaussian noise", Fluctuation and Noise Letters, 6(4):C33-C36.
    [ abstract]

  4. A Relano, J Retamosa, E Faleiro, RA Molina, AP Zuker (2006), "1/f noise and very high spectral rigidity", Physical Review E, 73:026204.

    + 2005

  5. JW Kirchner (2005), "Aliasing in 1/falpha noise spectra: origins, consequences, and remedies", Physical Review E, 71:066110. Erratum in: 71:069902.

    + 2003

  6. JB Gao, YH Cao, JM Lee (2003), "Principal component analysis of 1/f noise", Physics Letters A, 314:392-400.
    [PDF]

    + 2002

  7. T Antal, M Droz, G Gyorgyi, Z Racz (2002), "Roughness distributions for 1/fa signals", Physical Review E, 65:046140. arxiv.org preprint, cond-mat/0112277.
    [abstract] [ PDF]

  8. L Du, YQ Zhuang (2002), "Singularity comparison between 1/f fluctuations with statistical analysis of wavelet maxima", Physica A, 173:52-58.
    [ abstract]

  9. MJ Fadili, ET Bullmore (2002), "Wavelet-generalized least squares: a new BLU estimator of linear regression models with 1/f errors", NeuroImage, 15:217-232.
    [ PDF ]

  10. Octavio Miramontes, Pejman Rohani 92002), "Estimating 1/fa scaling exponents from short time-series", Physica D, 166:147-154.

  11. Carolyne M van Vliet (2002), "Random walk and 1/f noise", Physica A, 303:421-426.

    + 2001

  12. Z Gingl, S Ishioka, D Choi, N Fuchikami (2001), "Amplitude truncation of Gaussian 1/fa noises: Results and problems", Chaos, 11(3):619-623.

  13. D McClain (2001), "Numerical simulation of pink noise", preprint (Raytheon Missile Systems, Co.)
    [ PDF ]

    + 2000

  14. H Akabane, K Nakaya, M Agu (2000), "Asymmetrical property of 1/f resistance fluctuation for time reversion", Japanese Journal of Applied Physics, 39(5A):2865-2869.

  15. S Ishioka, Z Gingl, D Choi, N Fuchikami (2000), "Amplitude truncation of Gaussian 1/fa noises", Physics Letters A, 269:7-12.

  16. AV Yakimov, FN Hooge (2000), "A simple test of the Gaussian character of noise", Physica B, 291(2):97-104.

    + 1999

  17. H Akabane, M Agu, A Yoshida (1999), "Fractal characters of 1/2-order integration of white noise and 1/f resistance fluctuation", Japanese Journal of Applied Physics, 38(5A):3007-3010.

  18. T Saito, M Agu, M Yamada (1999), "A measure of complexity for 1/f fluctuation", Japanese Journal of Applied Physics, 38(5B):L596-L599.

    + 1998

  19. M Agu, M Tamada (1998), "Short-time information entropy as a complexity measure", Japanese Journal of Applied Physics, 37(11B):L1415-L1417.

  20. H Akabane, M Agu (1998), "Time-reversible property of 1/f fluctuation using higher-ord correlation function", Japanese Journal of Applied Physics, 37(7A):L830-L832.

  21. Brett Ninness (1998), "Estimation of 1/f noise", IEEE Transactions on Information Theory, 44(1):32-46.

  22. Berndt Pilgram, Daniel T Kaplan (1998), "A comparison of estimators for 1/f noise", Physica D, 114:108-122.

    + 1997

  23. FN Hooge, PA Bobbert (1997), "On the correlation function of 1/f noise", Physica B, 239:223-230.

  24. S Thurner, SB Lowen, MC Feurstein, C Heneghan, HG Feichtinger, MC Teich (1997), "Analysis, synthesis, and estimation of fractal-rate stochastic point processes", Fractals, 5(4):565-595.

    + 1995

  25. NJ Kasdin (1995), "Discreate simulation of colored noise and stochastic-processes and 1/f(alpha) power-law noise generation", Proceedings of the IEEE, 83(5):802-827.

  26. I Nagy, Z Gingl, LB Kiss (Kish), J Vinko (1995), "A method for testing first-order Markovian property of Gaussian phenomena including 1/f noise", Physica B, 216(1-2):79-84.

  27. MS Taqqu, V Teverovsky, W Willinger (1995), "Estimators for long-range dependence: an empirical study", Fractals, 3(4):785-798.

    + 1993

  28. M. Deriche, A.H. Tewfik, "Maximum likelihood estimation of the parameters of discrete fractionally differenced gaussian noise process", IEEE Transactions on Signal Processing, 41(10), 2977-2989 (1993).

  29. Paul Newbold, Christos Agiakloglou (1993), "Bias in the sample autocorrelations of fractional noise", Biometrika, 80(3):698-702.

    + 1992

  30. KP O'Brien, MB Weissman (1992), "Statistical signatures of self-organization", Physical Review A, 46(8):R4475-R4478.

  31. GW Wornell (1992), "Wavelet-based representations fot the 1/f family of fractal processes", Proceedings of the IEEE, 81:1428-1450.

    + 1991

  32. NP Greis , HS Greenside (1991), "Implication of a power-law power spectrum for self-affinity", Physical Review A, 44:2324-2334.

  33. E Masry (1991), "Flicker noise and the estimation of the Allan variance", IEEE Transactions on Information Theory, 37(4):1173-1177.
    [abstract]

  34. James Theiler (1991), "Some comments on the correlation dimension of 1/fa noise", Physics Letters A, 155:480-493.

    + 1990

  35. Steven B Lowen , Malvin C Teich (1990), "Power-law shot noise", IEEE Transactions on Information Theory, 36(6):1302-1318.

  36. Gregory Wornell (1990), "A Karhunen-Loeve-like expansion for 1/f processes via wavelets", IEEE Transactions on Information Theory, 36(4):859-861.

    + 1989

  37. SB Lowen, MC Teich (1989), "Generalised 1/f shot noise", IEE Electronic Letters, 25:1072-1074.

  38. SB Lowen, MC Teich (1989), "Fractal shot noise", Physical Review Letters, 25:1755-1759.
    [abstract]

  39. AR Osborne, A Provenzale (1989), "Finite correlation dimension for stochastic systems with power-law spectra", Physica D, 35:357-381.

    + 1987

  40. H Takayasu (1987), "f-b power spectrum and stable distribution", Journal of the Physical Society of Japan, 56(4):1257-1260.

    + 1986

  41. T Lundahl, WJ Ohley, SM Kay, R Stiffert (1986), "Fractional brownian motion: a maximum likelihood estimator and its application to image texture," IEEE Transactions on Medical Imaging, 5(3):152-161.

    + 1984

  42. G.N.Bochkov, Yu.E.Kuzovlev (1984), "On the probabilistic characteristics of 1/f-noise",
    Izvestiya VUZov.-Radiofizika, 27, 1151-. Translation in English in "Radiophysics and Quantum Electronics".

    + 1980

  43. CW Granger, R Joyeux, "An introduction to long memory time series models and fractional differencing", Journal of Time Series Analysis, 1(1):15-29 (1980).

    + 1978

  44. RF Voss, "Linearity of 1/f noise mechanism", Physical Review Letters, 40(14):913-916 (1978).

    + 1976

  45. J.L. Tandon, H.R. Bilger (1976), "1/f noise as a non-stationary process: experimental evidences and some analytical conditions", Journal of Applied Physics, 47:1697-1701.

    + 1975

  46. PH Handel (1975), "1/f noise - an 'infrared' phenomenon", Physical Review Letters, 34:1492-1495.

    + 1968

  47. James J Brophy (1968), "Statistics of 1/f noise", Physical Review, 166(3):827-831.
    [abstract]

  48. I Flinn (1968), "Extent of the 1/f noise spectrum", Nature, 219:1356-1357.
    [abstract]

    + 1967

  49. BB Mandebrot (1967), "Some noise with 1/f spectrum: a bridge between direct current and white noise", IEEE Transaction of Information Theory, 13:289-298.

    + 1966

  50. JA Barnes, DW Allan (1966), "A statistical model of flicker noise", Proceedings of the IEEE, 54:176-178.