A Sampling Theorem For Signals Band-Limited To A General Domain In Several Dimensions
Abbreviated Journal Title
J. Math. Anal. Appl.
STURM-LIOUVILLE PROBLEMS; LAGRANGE INTERPOLATION; Mathematics, Applied; Mathematics
Sampling series expansions for functions (signals) that are bandlimited to N-dimensional rectangles (N greater-than-or-equal-to 1) have been studied extensively; however, if a function is bandlimited to a general region in R(N), not much is known about its sampling series expansion. In this paper, we derive a sampling theorem for functions that are bandlimited (in the sense of Kramer) to finite regions with smooth boundaries in R(N). The sampling series expansions obtained for these functions are Lagrange-type interpolation series. Our technique utilizes Green's function of the region involved. As an application of our sampling theorem, we obtain a new method for summing infinite series in several variables. (C) 1994 Academic Press, Inc.
Journal of Mathematical Analysis and Applications
"A Sampling Theorem For Signals Band-Limited To A General Domain In Several Dimensions" (1995). Faculty Bibliography 1990s. 1254.