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.

Efficient line spectral estimation methods applicable to sub-Nyquist sampling are drawing considerable attention in both academia and industry. In this letter, we propose an enhanced compressed sensing (CS) framework for line spectral estimation, termed sparsity-based compressed covariance sensing (SCCS). In terms of sampling, SCCS is implemented by periodic non-uniform sampling; In terms of recovery, SCCS focuses on compressed line spectral recovery using covariance information. Due to the dual priors on sparsity and structure, SCCS theoretically performs better than CS in compressed line spectral estimation. We explain this superiority from the mutual incoherence perspective: the sensing matrix in SCCS has a lower mutual coherence than that in classic CS. Extensive experimental results show a high consistency with the theoretical inference. All in all, SCCS opens many avenues for line spectral estimation.

Multiple signal classification (MUSIC) has gained prominence in frequency estimation with the virtue of overcoming the undersampling problem of blade tip timing (BTT). However, as a crucial vibration feature, the amplitude cannot be estimated by MUSIC. Existing amplitude extraction methods for MUSIC are performed as postprocessing methods not related to MUSIC. Additionally, existing derivations of MUSIC for real signals use Euler’s formula to transform real signals into complex exponential signals. Therefore, this article rederives MUSIC based solely on real signals and further proposes an amplitude-identifiable MUSIC (Aid-MUSIC) approach to recover the amplitude information hidden in the eigenvalue decomposition of MUSIC. Combined with the proposed formulaic explanation of MUSIC’s asynchronous-pass ability, Aid-MUSIC is adapted according to the characteristics of BTT signal. The simulations and experiments show that Aid-MUSIC can achieve the simultaneous and stable extraction of amplitude and frequency for asynchronous frequency components without the interference of synchronous frequency components.