Discrete Estimation of Spectral Density for Alpha Stable Signals Observed with an Additive Error
References:
[1] S. Cambanis, (1983) “Complex symetric stable variables and processes” In P.K.SEN, ed, Contributions to Statistics”: Essays in Honour of Norman L. Johnson North-Holland. New York,(P. K. Sen. ed.), pp. 63-79
[2] S. Cambanis and M. Maejima (1989). “Two classes of self-similar stable processes with stationary increments”. Stochastic Process. Appl. Vol. 32, pp. 305-329
[3] M.B. Marcus and K. Shen (1989). “Bounds for the expected number of level crossings of certain harmonizable infinitely divisible processes”. Stochastic Process. Appl., Vol. 76, no. 1 pp 1-32.
[4] E. Masry, S. Cambanis (1984). “Spectral density estimation for stationary stable processes”. Stochastic processes and their applications, Vol. 18, pp. 1-31 North-Holland.
[5] G. Samorodnitsky and M. Taqqu (1994). “Stable non Gaussian processes ». Chapman and Hall, New York.
[6] K., Panki and S. Renming (2014). “Stable process with singular drift”. Stochastic Process. Appl., Vol. 124, no. 7, pp. 2479-2516
[7] C. Zhen-Qing and W. Longmin (2016). “Uniqueness of stable processes with drift.” Proc. Amer. Math. Soc., Vol. 144, pp. 2661-2675
[8] K. Panki, K. Takumagai and W. Jiang (2017). “Laws of the iterated logarithm for symmetric jump processes”. Bernoulli, Vol. 23, n° 4 pp. 2330-2379.
[9] M. Schilder (1970). “Some Structure Theorems for the Symmetric Stable Laws”. Ann. Math. Statist., Vol. 41, no. 2, pp. 412-421.
[10] R. Sabre (2012b). “Missing Observations and Evolutionary Spectrum for Random”. International Journal of Future Generation Communication and Networking, Vol. 5, n° 4, pp. 55-64.
[11] E. Sousa (1992). “Performance of a spread spectrum packet radio network link in a Poisson of interferences”. IEEE Trans. Inform. Theory, Vol. 38, pp. 1743-1754
[12] M. Shao and C.L. Nikias (1993). “Signal processing with fractional lower order moments: Stable processes and their applications”, Proc. IEEE, Vol.81, pp. 986-1010
[13] C.L. Nikias and M. Shao (1995). “Signal Processing with Alpha-Stable Distributions and Applications”. Wiley, New York
[14] S. Kogon and D. Manolakis (1996). “Signal modeling with self-similar alpha- stable processes: The fractional levy motion model”. IEEE Trans. Signal Processing, Vol 44, pp. 1006-1010
[15] N. Azzaoui, L. Clavier, R. Sabre, (2002). “Path delay model based on stable distribution for the 60GHz indoor channel” IEEE GLOBECOM, IEEE, pp. 441-467
[16] J.P. Montillet and Yu. Kegen (2015). “Modeling Geodetic Processes with Levy alpha-Stable Distribution and FARIMA”, Mathematical Geosciences. Vol. 47, no. 6, pp. 627-646.
[17] M. Pereyra and H. Batalia (2012). “Modeling Ultrasound Echoes in Skin Tissues Using Symmetric alpha-Stable Processes”. IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, Vol. 59, n°. 1, pp. 60-72.
[18] X. Zhong and A.B. Premkumar (2012). “Particle filtering for acoustic source tracking in impulsive noise with alpha-stable process”. IEEE Sensors Journal, Vol. 13, no. 2, pp. 589 - 600.
[19] Wu. Ligang and W. Zidong (2015). “Filtering and Control for Classes of Two-Dimensional Systems”. The series Studies in Systems of, Decision and Control, Vol.18, pp. 1-29.
[20] N. Demesh (1988). “Application of the polynomial kernels to the estimation of the spectra of discrete stable stationary processes”. (Russian) Akad.Nauk.ukrain. S.S.R. Inst.Mat. Preprint 64, pp. 12-36
[21] F. Brice, F. Pene, and M. Wendler, (2017) “Stable limit theorem for U-statistic processes indexed by a random walk”, Electron. Commun. Prob., Vol. 22, no. 9, pp.12-20.
[22] R. Sabre (2019). “Alpha Stable Filter and Distance for Multifocus Image Fusion”. IJSPS, Vol. 7, no. 2, pp. 66-72.
[23] JN. Chen, J.C. Coquille, J.P. Douzals, R. Sabre (1997). “Frequency composition of traction and tillage forces on a mole plough”. Soil and Tillage Research, Vol. 44, pp. 67-76.
[24] R. Sabre (1995). “Spectral density estimate for stationary symmetric stable random field”, Applicationes Mathematicaes, Vol. 23, n°. 2, pp. 107-133
[25] R. Sabre (2012a). “Spectral density estimate for alpha-stable p-adic processes”. Revisita Statistica, Vol. 72, n°. 4, pp. 432-448.
[26] R. Sabre (2017). “Estimation of additive error in mixed spectra for stable prossess”. Revisita Statistica, Vol. LXXVII, n°. 2, pp. 75-90.
[27] R. Sabre (2019) “Aliasing Free and Additive Error in Spectra for Alpha Stable Signals”, International Journal of Electrical and Computer Engineering, Vol. 13, No. 10, pp. 668-673.
[28] E. Masry, (1978). “Alias-free sampling: An alternative conceptualization and its applications”, IEEE Trans. Information theory, Vol. 24, pp.317-324.
[29] A. Janicki and A. WERON (1993). “Simulation and Chaotic Behavior of Alpha-stable Stochastic Processes”. Series: Chapman and Hall/CRC Pure and Applied Mathematics, New York.
