Optimal sub-Nyquist nonuniform sampling and reconstruction for multiband signals

Abstract

We study the problem of optimal sub-Nyquist sampling for perfect reconstruction of multiband signals. The signals are assumed to have a known spectral support that does not tile under translation. Such signals admit perfect reconstruction from periodic nonuniform sampling at rates approaching Landau's lower bound equal to the measure of. For signals with sparse , this rate can be much smaller than the Nyquist rate. Unfortunately, the reduced sampling rates afforded by this scheme can be accompanied by increased error sensitivity. In a recent study, we derived bounds on the error due to mismodeling and sample additive noise. Adopting these bounds as performance measures, we consider the problems of optimizing the reconstruction sections of the system, choosing the optimal base sampling rate, and designing the nonuniform sampling pattern. We find that optimizing these parameters can improve system performance significantly. Furthermore, uniform sampling is optimal for signals with that tiles under translation. For signals with nontiling , which are not amenable to efficient uniform sampling, the results reveal increased error sensitivities with sub-Nyquist sampling. However, these can be controlled by optimal design, demonstrating the potential for practical multifold reductions in sampling rate.

Assessment of sub-Nyquist deterministic and random data sampling techniques for operational modal analysis

“…It is desired to sample x(t) at a rate lower than the Nyquist sampling rate 1/Τ (in Hz), and still be able to obtain a useful estimate of the power spectrum Px(ω). To this aim, the multi-coset sampling is adopted 29,30 at stage I, according to which the uniform grid of selected at a deterministically pre-specified position which remains the same for all blocks.…”

“…In particular, the method treats signals as realizations of an underlying wide-sense stationary random process and estimates second-order statistics (i.e., the covariance matrix or, 6 equivalently, the PSD matrix) through a power spectrum blind sampling (PSBS) step assuming a deterministic periodic non-uniform-in-time sampling scheme known as multi-coset sampling [29][30][31][32] .…”

Efficient Recovery of Sub-Nyquist Sampled Sparse Multi-Band Signals Using Reconfigurable Multi-Channel Analysis and Modulated Synthesis Filter Banks

“…For the CNUS approach, it is known that the reconstruction can be done, in principle, via a set of ideal multi-level synthesis filters, given the sampling pattern [7]- [9]. The related problem of selecting the optimal sampling patterns has also been addressed [9]- [11]. However, the straightforward CNUS recovery scheme has very high design and implementation complexities 1 .…”

“…Given K samples in each block (period) of M samples, (K < M ), the problem is to recover the M − K missing samples. For the CNUS approach, it is known that the reconstruction can be done, in principle, via a set of ideal multi-level synthesis filters, given the sampling pattern [7]- [9]. The related problem of selecting the optimal sampling patterns has also been addressed [9]- [11].…”

A new airborne self-protection jammer for countering ground radars based on sub-Nyquist

“…So subnyquist sampling has been developed and utilized in several applications such as data compression [10], medical imaging [11] and radar imaging [12]. Undersampling at low rates can lead to aliasing, and the corresponding reconstruction algorithm should be addressed to be a prior condition [13]. Inspired by this characteristic, Ref.…”