Delay Coprime Sampling: A Simplified Sub-Nyquist Sampling for Noisy Multi-Sinusoidal Signals

As the frequencies increase, the Nyquist rate is difficult to reach in certain applications. Consequently, alternatives to high-rate sampling are drawing considerable attention. In this letter, we propose a novel sub-Nyquist sampling scheme for noisy multi-sinusoidal signal (MSS), termed delay coprime sampling (DCS). In terms of structure, DCS is the simplest deterministic compressive blind sampling. Specifically, DCS is a periodic non-uniform sampling of order 2 with coprime delays. To estimate the frequency or power spectrum from extremely undersampled samples from DCS, we construct a new function, termed $n$th-fold correlation, which carries the same frequency set as the MSS. Remarkably, we find the $n$th-fold correlation samples with consecutive lags are available through step-by-step operations and then the power spectrum or characteristic frequency can be efficiently estimated. Extensive simulations are provided to verify the effectiveness of DCS. By comparing it with popular sub-Nyquist schemes, DCS shows advantages in reducing sampling rate/channel while simplifying the hardware configuration.