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Song, Zhan-jie; Sun, Wen-chang; Yang, Shou-yuan; Zhu, Guang-wen

Approximation of weak sense stationary stochastic processes from local averages. (English) Zbl 1122.60039

Sci. China, Ser. A 50, No. 4, 457-463 (2007).
Summary: We show that a weak sense stationary stochastic process can be approximated by local averages. Explicit error bounds are given. Our result improves an early one fromW. Splettstösser, R. L. Stens and G. Wilmes [Funct. Approximatio, Comment. Math. 11, 39–56 (1981; Zbl 0481.42007)].

Cited in 5 Documents

MSC:

60G10 Stationary stochastic processes
42C15 General harmonic expansions, frames
94A20 Sampling theory in information and communication theory

Keywords:

sampling theorem; weak sense stationary stochastic processes; local averages; average sampling

Citations:

Zbl 0481.42007
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Full Text: DOI

References:

[1] Splettstösser W. Sampling series approximation of continuous weak sense stationary processes. Information and Control, 50: 228–241 (1981) · Zbl 0497.60032 · doi:10.1016/S0019-9958(81)90343-0
[2] Marvasti F. Nonuniform Sampling. Theory and Practice. New York: Kluwer Academic, 2001, 123–168
[3] Li Z, Wu R. A Course of Studies on Stochastic Processes. Beijing: Higher Education Press, 1987. 291 (in Chinese)
[4] Gröchenig K. Reconstruction algorithms in irregular sampling. Math Comput, 59: 181–194 (1992) · Zbl 0756.65159
[5] Butzer P L, Lei J. Errors in truncated sampling series with measured sampled values for non-necessarily bandlimited functions. Funct Appro, 26: 25–39 (1998) · Zbl 0982.94008
[6] Butzer P L, Lei J. Approximation of signals using measured sampled values and error analysis. Commun Appl Anal, 4: 245–255 (2000) · Zbl 1089.94503
[7] Sun W, Zhou X. Reconstruction of bandlimited functions from local averages. Constr Approx, 18: 205–222 (2002) · Zbl 1002.42022 · doi:10.1007/s00365-001-0011-y
[8] Sun W, Zhou X. Reconstruction of bandlimited signals from local averages. IEEE Trans Inform Theory, 48: 2955–2963 (2002) · Zbl 1062.94538 · doi:10.1109/TIT.2002.804047
[9] Sun W, Zhou X. Reconstruction of functions in spline subspaces from local averages. Proc Amer Math Soc, 131: 2561–2571 (2003) · Zbl 1026.94004 · doi:10.1090/S0002-9939-03-07082-5
[10] Sun W, Zhou X. Average sampling theorem for shift invariant subspaces. Science in China Ser E, 43: 524–530 (2000) · Zbl 1232.94011
[11] Song Z, Yang S, Zhou X. Approximation of signals from local averages. Applied Mathematics Letters, 19: 1414–1420 (2006) · Zbl 1132.94305 · doi:10.1016/j.aml.2006.01.018
[12] Song Z, Zhou X, He G. Error estimate on non-bandlimited random signals by local averages. Lecture Notes in Computer Science, 3391: 822–825 (2006) · doi:10.1007/11758501_114
[13] Splettstösser W, Stens R L, Wilmes G. On the approximation of the interpolating series of G Valiron. Funct Approx Comment Math, 11: 39–56 (1980) · Zbl 0481.42007
[14] Pinsky M A. Introduction to Fourier Analysis and Wavelets. Pacific Grove, Wadsworth Group, Brooks/Cole, 2002, 176 · Zbl 1065.42001
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