Error analysis in sampling theory

Abstract

A basic problem in signal theory is the reconstruction of a band-limited function f(t) from its sampled value f(nT). Because of a number of errors, the computed or physically realized signal is only approximately equal to f(t). The most common sampling errors are: round-off of f(nT), truncation of the series generating f(t), aliasing of frequency components above half the sampling rate 1/T, jitter in the recording times nT, loss of a number of sampled values, and imperfect filtering in the recovery of f(t). In the following we study the effect of these errors on the reconstructed signal and its Fourier transform.