Fast Reconstruction Algorithms for Periodic Nonuniform Sampling with Applications to Time-Interleaved ADCs

A bandlimited signal can be reconstructed from its periodic nonuniformly spaced samples provided the average sampling rate is at least the Nyquist rate. Unlike many previously published methods, the algorithm derived in this paper is designed that pays special attention to various practical constraints. In particular, we propose a fast and numerically robust reconstruction method which can utilize FIR filters with a small number of taps and requires only a modest amount of oversampling to achieve high accuracy. The efficiency and accuracy of the algorithm is obtained by fully exploiting the sampling structure combined with utilizing localized Fourier analysis. We discuss applications in time-interleaved analog-to-digital converters where nonuniform periodic sampling arises due to timing mismatches. Finally, numerical simulations demonstrate the performance of our algorithm.