Nonuniform sampling of bandlimited signals with polynomial growth on the real axis

We derive a sampling expansion for bandlimited signals with polynomial growth on the real axis. The sampling expansion uses nonuniformly spaced sampling points. But unlike other known sampling expansions for such signals, ours converge uniformly to the signal on any compact set. An estimate of the truncation error of such a series is also obtained.

[1]  Alan J. Lee.  Characterization of Bandlimited Functions and Processes , 1976, Inf. Control..

[2]  Helly.  Fourier transforms in the complex domain , 1936 .

[3]  H. Feichtinger,et al.  Irregular sampling theorems and series expansions of band-limited functions , 1992 .

[4]  A. Zemanian.  Generalized Integral Transformations , 1987 .

[5]  A. C. Sim,et al.  Distribution Theory and Transform Analysis , 1966 .

[6]  L. Campbell.  Sampling Theorem for the Fourier Transform of a Distribution with Bounded Support , 1968 .

[7]  A. Zayed.  Advances in Shannon's Sampling Theory , 1993 .

[8]  Moshe Zakai,et al.  Band-Limited Functions and the Sampling Theorem , 1965, Inf. Control..

[9]  R. F. Hoskins,et al.  Sampling Expansions for Functions Band-Limited in the Distributional Sense , 1984 .

[10]  Allan G. Piersol,et al.  Advances in Shannon’s Sampling Theory , 1994 .

[11]  G. Walter.  Sampling Bandlimited Functions of Polynomial Growth , 1988 .

[12]  N. Wiener,et al.  Fourier Transforms in the Complex Domain , 1934 .

[13]  Ernst Pfaffelhuber,et al.  Sampling series for band-limited generalized functions , 1971, IEEE Trans. Inf. Theory.

[14]  G. Walter.  Nonuniform sampling of bandlimited functions of polynomial growth , 1992 .

[15]  Sanjeev R. Kulkarni,et al.  Covering numbers for real-valued function classes , 1997, IEEE Trans. Inf. Theory.

[16]  H. Feichtinger,et al.  Iterative reconstruction of multivariate band-limited functions from irregular sampling values , 1992 .