Reconstruction of nonuniformly sampled bandlimited signals by means of digital fractional delay filters

This paper considers the problem of reconstructing a class of nonuniformly sampled bandlimited signals of which a special case occurs in, e.g., time-interleaved analog-to-digital converter (ADC) systems due to time-skew errors. To this end, we propose a synthesis system composed or digital fractional delay filters. The overall system (i.e., nonuniform sampling and the proposed synthesis system) can be viewed as a generalization of time-interleaved ADC systems to which the former reduces as a special case. Compared with existing reconstruction techniques, our method has major advantages from an implementation point of view. To be precise, (1) we can perform the reconstruction as well as desired (in a certain sense) by properly designing the digital fractional delay filters, and (2) if properly implemented, the fractional delay filters need not be redesigned in case the time skews are changed. The price to pay for these attractive features is that we need to use a slight oversampling. It should be stressed, however, that the oversampling factor is less than two as compared with the Nyquist rate. The paper includes error and quantization noise analysis. The former is useful in the analysis of the quantization noise and when designing practical fractional delay filters approximating the ideal filters.