Maximal gap of a sampling set for the exact iterative reconstruction algorithm in shift invariant spaces

A conventional A/D converter prefilters a signal by an ideal lowpass filter and performs sampling for bandlimited signals by the Nyquist sampling rate. Recent research reveals that A/D conversion in a shift invariant space provides more flexible choices for designing a practical A/D conversion system of high accuracy. This paper focuses on the maximal gap of a sampling set for the iterative algorithm in shift invariant spaces, which provides an explicit formula to calculate the maximal gap of a sampling set in terms of a generator of the undertaken shift invariant spaces.