Sampling Error Analysis and Properties of Non-bandlimited Signals That Are Reconstructed by Generalized Sinc Functions

TL;DR

This paper analyzes the reconstruction error of non-bandlimited signals using generalized sinc functions, considering adaptive truncation and noise effects, and explores the mathematical properties of these signals.

Contribution

It provides a detailed error analysis for non-bandlimited signal reconstruction with generalized sinc functions, including noise impact and function space properties.

Findings

Error bounds for adaptive truncation schemes

Estimation of error expectation and variance with noise

Reproducing properties and Sobolev smoothness of signal space

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 article 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.