Interpolation of bandlimited functions from quantized irregular samples

The problem of reconstructing a /spl pi/-bandlimited signal f from its quantized samples taken at an irregular sequence of points (t/sub k/)/sub k/spl isin//spl Zopf// arises in oversampled analog-to-digital conversion. The input signal can be reconstructed from the quantized samples (f(t/sub k/))/sub k/spl isin//spl Zopf// by estimating samples (f(n//spl lambda/))/sub n/spl isin//spl Zopf//, where /spl lambda/ is the average uniform density of the sequence (tk)/sub k/spl isin//spl Zopf//, assumed here to be greater than one, followed by linear low-pass filtering. We study three techniques for estimating samples (f(n//spl lambda/))/sub n/spl isin//spl Zopf// from quantized irregular samples (f(t/sub k/))/sub k/spl isin//spl Zopf//, including Lagrangian interpolation, and two other techniques which result in a better overall accuracy of oversampled A/D conversion.