Sampling error analysis and some properties of non-bandlimited signals that are reconstructed by generalized sinc functions

Abstract

Recently, efforts have been made to use generalized sinc functions to perfectly reconstruct various kinds of non-bandlimited signals. As a consequence, perfect reconstruction sampling formulas have been established using such generalized sinc functions. This paper studies the error of the reconstructed non-bandlimited signal when an adaptive truncation scheme is employed. Further, when there are noises present in the samples, estimation on the expectation and variance of the error pertinent to the reconstructed signal is also given. Finally discussed are the reproducing properties and the Sobolev smoothness of functions in the space of non-bandlimited signals that admits such a sampling formula.

Keywords:

• generalized sinc function
• non-bandlimited signal
• sampling theorem
• truncated error
• noisy error
• reproducing property
• Sobolev smoothness

AMS Subject Classifications:

• 41
• 65

Acknowledgments

Li is supported by the National Natural Science Foundation of China (Grant No.11126343), Natural Scientific Project of Guangxi University under grant XBZ110572 and by Macao Science and Technology Fund FDCT/056/2010/A3 for his postdoctoral research. Chen is supported by NSFC under grant 61072126 and by Natural Science Foundation of Guangdong Province under grant S2011010004986. Qian is supported by Grant of University of Macau UL017/08-Y3/MAT/QT01/FST and by Macao Science and Technology Fund FDCT/056/2010/A3.