Robust reconstruction of nonuniformly sampled signals

The presented method solves the problem of reconstructing nonuniformly sampled signals using an efficient approach. It is aimed to process signals sequentially, not in blocks, and is suitable for implementation in real-time. The considered signals are continuously sampled with a periodic sampling pattern. The method is well suited for extremely uneven sampling, e.g. all samples are concentrated in 1/4 of the periodic sampling pattern, while % are devoid of samples. The ideal reconstruction of such nonuniformly sampled signals employing analytical solutions is theoretically possible but useless in practical applications. The well known approximation using a Fourier series results in aliasing, if the bandwidth of the signal is larger than half the inverse of the sampling-pattern period, no matter how many samples are taken within the period. The paper presents a method that works well in practical applications and avoids aliasing. It uses a special function series approach to describe the signal in its entirety and with extended bandwidth compared to the Fourier series. The function series parameters are estimated efficiently in real-time using multi-rate signal processing. The approach is compared to other methods with respect to performance and computational complexity and proves to be overall superior to these.