RECONSTRUCTION OF BAND-LIMITED SIGNALS FROM IRREGULAR SAMPLES

The classical theorem of Shannon enables one to reconstruct a finite-e nergy, bandlimited signal from a set of regularly spaced samples. Rece ntly, Benedetto and Heller applied the theory of frames to derive a se ries of sampling theorems with irregularly spaced sampling sequences. In this paper, we study one of these theorems with emphasis on its imp lementation. To implement the theorem, sampling sequences and sampled coefficients are required. Here, general schemes to construct sampling sequences, and to evaluate sampled coefficients, are established. In addition, we provide an error analysis on the approximation of sampled coefficients. Numerical results are furnished to illustrate the theor y and to study various related issues. These issues include the choice of sampling sequences and functions, the effect of truncating the sam pling formula, and the influence of the irregularity of sampling seque nces.