Reconstruction of Periodic Band Limited Signals from Non-Uniform Samples with Sub-Nyquist Sampling Rate

A Phase-Sensitive Optical Time Domain Reflectometry with Non-Uniform Frequency Multiplexed NLFM Pulse

In the domain of optical fiber distributed acoustic sensing, the persistent challenge of extending sensing distances while concurrently improving spatial resolution and frequency response range has been a complex endeavor. The amalgamation of pulse compression and frequency division multiplexing methodologies has provided certain advantages. Nevertheless, this approach is accompanied by the drawback of significant bandwidth utilization and amplified hardware investments. This study introduces an innovative distributed optical fiber acoustic sensing system aimed at optimizing the efficient utilization of spectral resources by combining compressed pulses and frequency division multiplexing. The system continuously injects non-linear frequency modulation detection pulses spanning various frequency ranges. The incorporation of non-uniform frequency division multiplexing augments the vibration frequency response spectrum. Additionally, nonlinear frequency modulation adeptly reduces crosstalk and enhances sidelobe suppression, all while maintaining a favorable signal-to-noise ratio. Consequently, this methodology substantially advances the spatial resolution of the sensing system. Experimental validation encompassed the multiplexing of eight frequencies within a 120 MHz bandwidth. The results illustrate a spatial resolution of approximately 5 m and an expanded frequency response range extending from 1 to 20 kHz across a 16.3 km optical fiber. This achievement not only enhances spectral resource utilization but also reduces hardware costs, making the system even more suitable for practical engineering applications.

Embracing off-the-grid samples

Many empirical studies suggest that samples of continuous-time signals taken at locations randomly deviated from an equispaced grid (i.e., off-the-grid) can benefit signal acquisition, e.g., undersampling and anti-aliasing. However, explicit statements of such advantages and their respective conditions are scarce in the literature. This paper provides some insight on this topic when the sampling positions are known, with grid deviations generated i.i.d. from a variety distributions. By solving a square-root LASSO decoder with an interpolation kernel we demonstrate the capabilities of nonuniform samples for compressive sampling, an effective paradigm for undersampling and anti-aliasing. For functions in the Wiener algebra that admit a discrete s-sparse representation in some transform domain, we show that O ( s poly log N ) random off-the-grid samples are sufficient to recover an accurate N 2 -bandlimited approximation of the signal. For sparse signals (i.e., s ≪ N ), this sampling complexity is a great reduction in comparison to equispaced sampling where O ( N ) measurements are needed for the same quality of reconstruction (Nyquist-Shannon sampling theorem). We further consider noise attenuation via oversampling (relative to a desired bandwidth), a standard technique with limited theoretical understanding when the sampling positions are non-equispaced. By solving a least squares problem, we show that O ( N log N ) i.i.d. randomly deviated samples provide an accurate N 2 -bandlimited approximation of the signal with suppression of the noise energy by a factor ∼ 1 log ( N ) .

Research on a step delay method in sequential equivalent time sampling (ETS)

Sequential equivalent time sampling (ETS) has been extensively used in data acquisition instruments (e.g., sampling oscilloscopes and time domain reflectometers). A novel step delay method is proposed based on the frequency difference to obtain a higher sampling rate in sequential ETS. It is different from the classic step delay methods and is capable of increasing the sampling rate. The sampling clock and the repetitive signal are taken as examples in this study. The time-frequency conversion relationship indicates that a fine step delay will be generated in the time domain if there is a frequency difference between the two in the frequency domain. The core of the proposed method is the selection of the appropriate frequency difference (step delay) according to the desired equivalent sampling rate. Two experiments were performed to verify the proposed method. The feasibility of the proposed method is verified using a digital storage oscilloscope. Four cases are examined in the experiment, and the final equivalent sampling rate is obtained as 5 PS/s for the equivalent sampling of a 4.999 995 GHz (or higher) signal. A data acquisition system with a 10 MS/s real-time sampling rate is designed to verify the feasibility of the proposed method, obtaining a theoretical equivalent sampling rate of 585 GS/s. The theoretical equivalent sampling rate and the examined equivalent sampling rate are consistent. The equivalent sampling waveform and real-time sampling waveform of a 1 GHz signal are compared, and the comparison result suggests that the proposed method can acquire more waveform information. The proposed method obtains a high equivalent sampling rate for repetitive signals, and techniques (e.g., oversampling) are given to obtain higher vertical resolution. The proposed method, combined with a sample-and-hold amplifier, can also achieve a higher analog bandwidth.

Calling the amino acid sequence of a protein/peptide from the nanospectrum produced by a sub-nanometer diameter pore

The blockade current that develops when a protein translocates across a thin membrane through a sub-nanometer diameter pore informs with extreme sensitivity on the sequence of amino acids that constitute the protein. The current blockade signals measured during the translocation are called a nanospectrum of the protein. Whereas mass spectrometry (MS) is still the dominant technology for protein identification, it suffers limitations. In proteome-wide studies, MS identifies proteins by database search but often fails to provide high protein sequence coverage. It is also not very sensitive requiring about a femtomole for protein identification. Compared with MS, a sub-nanometer diameter pore (i.e. a sub-nanopore) directly reads the amino acids constituting a single protein molecule, but efficient computational tools are still required for processing and interpreting nanospectra. Here, we delineate computational methods for processing sub-nanopore nanospectra and predicting theoretical nanospectra from protein sequences, which are essential for protein identification.