Abstract
An extension of the sampling theorem to multi-band signals is discussed and an application to the compression of speech outlined.
Similar content being viewed by others
References
M. G. Beaty and M. M. Dodson. The distribution of sampling rates for signals with equally spaced, equally wide spectral bands. SIAM J. Appl. Math., 53 (1993), 893–906.
M. G. Beaty, M. M. Dodson, and J. R. Higgins. Approximating Paley-Wiener functions by smoothed step functions. J. Approx. Th., 78 (1994) 433–445.
M. G. Beaty and J. R. Higgins. Aliasing and Poisson summation in the sampling theory of Paley-Wiener spaces. J. Fourier Analysis and Applic, 1 (1994), 67–85.
P. Butzer and A. Gessinger. The approximate sampling theorem, Poisson’s sum formula, a decomposition theorem for Parseval’s equation and their interconnections. Workshop on Sampling Theory and Applications, Jurmala, Latvia, 1995.
P. L. Butzer. A survey of the Whittaker-Shannon sampling theorem and some of its extensions. J. Math. Res. Exposition, 3 (1983), 185–212.
P. L. Butzer, M. Hauss, and R. L. Stens. The sampling theorem and its unique role in various branches of mathematics. In Mathematical Sciences, Past and Present, 300 years of Mathematische Gesellschaft in Hamburg. Mitteilungen Math. Ges. Hamburg, Hamburg, 1990.
P. L. Butzer, W. Splettstöβer, and R. L. Stens. The sampling theorem and linear prediction in signal analysis. Jber. d. Dt. Math.-Verein., 3 (1988), 1–70.
P.L. Butzer and R.L. Stens. Predictiofn-bandlimitedsignalsfrompastsamplesintermsofsplinesoflowdegree.Math.Nachr. 132 (1987), 115–13
P. L. Butzer and R. L. Stens. Sampling theory for not necessarily band-limited functions: a historical overview. SIAM Review, 34 (1992), 40–53.
J. Clunie, Q. I. Rahman, and W. Walker. On entire functions of exponential type bounded on the real axis. Preprint, Université de Montréal, 1997.
M. Darnell, M. M. Dodson, B. Honary, and W. He. Adaptive-rate sampling applied to the storage and transmission of multiple band-pass signals. In Proc. Sixth Int. Conf. on System Engineering N. W. Bellamy (ed.), pp. 109-119, Coventry Polytechnic ICSE, 1988.
M. M. Dodson and A. M. Silva. Fourier analysis and the sampling theorem. Proc. Royal Irish Acad., 85A (1985), 81–108.
M. M. Dodson and A. M. Silva. An algorithm for optimal regular sampling. Signal Process., 17 (1989), 169–174.
R. Dodson. The Mauritius radio telescope and a study of selected supernova remnants associated with pulsars. PhD thesis, Durham University, Durham, UK, 1997.
J. R. Higgins. Five short stories about the cardinal series. Bull. Amer. Math. Soc, 12 (1985), 45–89.
J. R. Higgins. Sampling theory in Fourier and signal analysis: Foundations. Clarendon Press, Oxford, 1996.
A. J. Jerri. The Shannon sampling theorem — its various extensions and applications: a tutorial review. Proc. IEEE, 65 (1977), 1565–1596.
R. J. Marks II. Introduction to Shannon sampling and interpolation theory. Springer-Verlag, New York, 1991.
R. J. Marks II (ed.). Advanced topics in Shannon sampling and interpolation theory. Springer-Verlag, New York, 1993.
Q. I. Rahman and G. Schmeisser. The summation formulae of Poisson, Plana, Euler-Maclaurin and their relationship. J. Math. Sci. (Part I), 28 (1994), 151–171.
D. Sayre. Some implications of a theorem due to Shannon. Acta Cryst, 5 (1952), 834.
C. E. Shannon. A mathematical theory of communication. Bell Sys. Tech. J., 27 (1948), 379–423.
C. E. Shannon. Communication in the presence of noise. Proc. IRE, 37 (1949), 10–21.
D. Slepian. On bandwidth. Proc. IEEE, 64 (1976), 292–300.
H. Taub and D. L. Schilling. Principles of communication systems. McGraw Hill, New York, second edition, 1986.
R. G. Vaughan, N. L. Scott, and D. R. White. The theory of bandpass sampling. IEEE. Trans. Signal Processing, 39 (1991), 1973–1983.
Author information
Authors and Affiliations
Additional information
Dedicated to Paul Butzer to mark his seventieth birthday
Rights and permissions
About this article
Cite this article
Beaty, M.G., Dodson, M.M. An application of a general sampling theorem. Results. Math. 34, 241–254 (1998). https://doi.org/10.1007/BF03322054
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF03322054