Aliasing Error for Sampling Series Derivatives

Elements of Bernstein spaces of band-limited functions with band width σ, σ > 0 are perfectly sampled from their values at discrete set of points with different convergence criteria. The aliasing phenomenon occurs if the function is not band-limited or the sampling rate is lower than the band-width Nyquist rate), i.e σ → ∞. Since both conditions, band-limitedness and Nyquist rate are restrictive, it is desirable to find rigorous error estimates for the aliasing error. Here, several bounds for the aliasing error of sampling derivatives are established. We derive both uniform and Lp-norm bounds which are analogues of the results of Butzer et al. (2005), Fang (1996). Moreover, the so-called truncated aliasing error is investigated and a few numerical examples will be presented.