Whittaker-Kotelnikov-Shannon sampling theorem and aliasing error

Journal of Approximation Theory

Volumn 85, Issue 2, 1996, Pages 115-131

  Gensun, Fang ^a  

^a BEIJING NORMAL UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030140667     PISSN: 00219045     EISSN: None     Source Type: Journal    
DOI: 10.1006/jath.1996.0033     Document Type: Article

References (18)

1. 1. P. L. BUTZER, A survey of the Whittaker-Shannon sampling theorem and some of its extensions, J. Math. Res. Exposition 3 (1983), 185-212.
2. 2. J. R. HIGGINS, Five short stories about the cardinal series, Bull. Amer. Math. Soc. 12 (1985), 45-89.
3. 3. P. L. BUTZER AND W. SPLETTSTÖSSER, A sampling theorem for duration-limited functions with error estimates, Inform. and Control 34 (1977), 55-65.
4. 4. W. SPLETTSTÖSSER, Error estimates for sampling approximation of non-bandlimited functions, Math. Mech. Appl. Sci. 1 (1979), 127-137.
5. 5. J. L. BROWN, JR., On the error in reconstructing a non-bandlimited function by means of the bandpass sampling theory, J. Math. Anal. Appl. 18 (1967), 75-84; erratum 21 (1968), 699.
6. 6. S. M. NIKOLSKII, "Approximation of Functions of Several Variables and Imbedding Theorems," Springer-Verlag, Berlin/Heidelberg, New York, 1975.
7. p convergence of Lagrange interpolation of entire functions of exponential type, J. Approx. Theory 69 (1992), 302-317.
8. 8. J. MARCINKIEWICZ, Sur l'interpolation, I, Studia Math. 6 (1936), 1-17.
9. 9. N. I. ACHIESER, "Theory of Approximation," Ungar, New York, 1956.
10. 10. G. G. MAGARIL-IL'JAEV, Φ-average widths of function classes on the real axis, Uspekhi Mat. Nauk. 45 (1990), 211-212.
11. q(ℝ), J. Approx. Theory 73 (1994), 335-352.
12. p date, Indiana Univ. Math. J. 24 (1975), 677-689.
13. 13. R. P. BOAS, JR., "Entire Functions," Academic Press, New York, 1954.
14. 14. E. M. STEIN, Function of exponential type, Ann. of Math. 65 (1957), 582-593.
15. 15. A. F. TIMAN, "Theory of Approximation of Functions of a Real Variable," Pergamon, New York, 1963.
16. 16. S. RIES AND R. L. STENS, A localization principle for the approximation by sampling series, in "Proc. International Conference Theory of Approximation of Functions, Kiev, May 30-June 6, 1983" (N. P. Korneǐchuk et al., Eds.), pp. 507-509, Izdat. Nauka, Moscow, 1987.
17. 17. W. SPLETTSTÖSSER, R. L. STENS, AND G. WILMES, On approximation by the interpolation series of G. Valiron, Funct. Approx. Comment. Math. 11 (1981), 39-56.
18. 18. P. L. BUTZER AND R. L. STENS, Sampling theory for not necessarily band-limited functions: A historical overview, SIAM Rev. 34 (1992), 40-53.