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In this article, the tracking control problem for a class of nonlinear time‐delay systems is investigated. In particular, a new methodology for the design and the digital implementation of observer‐based tracking controllers is provided for a class of control‐affine nonlinear systems with state delays. First, a procedure for the design of continuous‐time observer‐based tracking controllers ensuring the global asymptotic stability of the corresponding closed‐loop tracking error system is provided for the considered class of systems. Then, sufficient conditions are provided for the existence of a suitably fast sampling and of an accurate quantization of the input/output channels such that the digital implementation of the proposed continuous‐time observer‐based tracking controller ensures the semi‐global practical stability property of the related sampled‐data quantized closed‐loop tracking error system, with arbitrarily small final target ball of the origin. Moreover, it is shown that, in the special case of delay‐free nonlinear systems, the sufficient conditions provided for the digital implementation of the proposed continuous‐time observer‐based tracking controller can be strongly relaxed. In the theory here developed, time‐varying sampling periods and nonuniform quantization of the input/output channels are taken into account. The proposed results are validated through examples concerning a class of neural networks systems and a class of time‐delay systems including, as a special case, a delay‐free actuated inverted pendulum. [ABSTRACT FROM AUTHOR]

Echo planar imaging (EPI) is a fast measurement technique commonly used in magnetic resonance imaging (MRI), but is highly sensitive to measurement non-idealities in reconstruction. Point spread function (PSF)-encoded EPI is a multi-shot strategy which alleviates distortion, but acquisition of encodings suitable for direct distortion-free imaging prolongs scan time. In this work, a model-based iterative reconstruction (MBIR) framework is introduced for direct imaging with PSF-EPI to improve image quality and acceleration potential. An MBIR platform was developed for accelerated PSF-EPI. The reconstruction utilizes a subspace representation, is regularized to promote local low-rankedness (LLR), and uses variable splitting for efficient iteration. Comparisons were made against standard reconstructions from prospectively accelerated PSF-EPI data and with retrospective subsampling. Exploring aggressive partial Fourier acceleration of the PSF-encoding dimension, additional comparisons were made against an extension of Homodyne to direct PSF-EPI in numerical experiments. A neuroradiologists' assessment was completed comparing images reconstructed with MBIR from retrospectively truncated data directly against images obtained with standard reconstructions from non-truncated datasets. Image quality results were consistently superior for MBIR relative to standard and Homodyne reconstructions. As the MBIR signal model and reconstruction allow for arbitrary sampling of the PSF space, random sampling of the PSF-encoding dimension was also demonstrated, with quantitative assessments indicating best performance achieved through nonuniform PSF sampling combined with partial Fourier. With retrospective subsampling, MBIR reconstructs high-quality images from sub-minute scan datasets. MBIR was shown to be superior in a neuroradiologists' assessment with respect to three of five performance criteria, with equivalence for the remaining two. A novel image reconstruction framework is introduced for direct imaging with PSF-EPI, enabling arbitrary PSF space sampling and reconstruction of diagnostic-quality images from highly accelerated PSF-encoded EPI data. [ABSTRACT FROM AUTHOR]

This paper proposes a hyperspectral imaging simulation method based on a ray-tracing algorithm. The algorithm combines calculations based on solar and atmospheric visible light radiation as well as the spectral bidirectional reflection distribution function (BRDF) of the target surface material and can create its own scenarios for simulation calculations on demand. Considering the presence of multiple scattering between the target and background, using the ray-tracing algorithm enables the precise computation of results involving multiple scattering. To validate the accuracy of the algorithm, we compared the simulated results with the theoretical values of the visible light scattering intensity from a Lambertian sphere. The relative error obtained was 0.8%. Subsequently, a complex scene of engineering vehicles and grass was established. The results of different observation angles and different coating materials were calculated and analyzed. In summary, the algorithm presented in this paper has the following advantages. Firstly, it is applicable to geometric models composed of any triangular mesh elements and accurately computes the effects of multiple scattering. Secondly, the algorithm combines the spectral BRDF information of materials and improves the efficiency of multiple scattering calculations using nonuniform sampling. The computed hyperspectral scattering data can be applied to simulate airborne or space-borne remote sensing data. [ABSTRACT FROM AUTHOR]

In this paper, the sampling and reconstruction problems in function subspaces of L p (R n) associated with the multi-dimensional special affine Fourier transform (SAFT) are discussed. First, we give the definition of the multi-dimensional SAFT and study its properties including the Parseval's relation, the canonical convolution theorems and the chirp-modulation periodicity. Then, a kind of function spaces are defined by the canonical convolution in the multi-dimensional SAFT domain, the existence and the properties of the dual basis functions are demonstrated, and the L p -stability of the basis functions is established. Finally, based on the nonuniform samples taken on a dense set, we propose an iterative reconstruction algorithm with exponential convergence to recover the signals in a L p -subspace associated with the multi-dimensional SAFT, and the validity of the algorithm is demonstrated via simulations. [ABSTRACT FROM AUTHOR]

Imaging maritime targets requires a high resolution and wide swath (HWRS) in a synthetic aperture radar (SAR). When operated with a variable pulse repetition interval (PRI), a staggered SAR can realize HRWS imaging, which needs to be reconstructed due to echo pulse loss and a nonuniformly sampled signal along the azimuth. The existing reconstruction algorithms are designed for stationary scenes in a staggered SAR mode, and thus, produce evident image defocusing caused by complex target motion for moving targets. Typically, the nonuniform sampling and complex motion of maritime targets aggravate the spectrum aliasing in a staggered SAR mode, causing inevitable ambiguity and degradation in its reconstruction performance. To this end, this study analyzed the spectrum of maritime targets in a staggered SAR system through theoretical derivation. After this, a reconstruction method named MBLCFD (Modified Best Linear Unbaised and Complex-Lag Time-Frequency Distribution) is proposed to refocus the blurred maritime target. First, the signal model of the maritime target with 3D rotation accompanying roll–pitch–yaw movement was established under the curved orbit of the satellite. The best linear unbiased (BLU) method was modified to alleviate the coupling of nonuniform sampling and target motion. A precise SAR algorithm was performed based on the method of inverse reversion to counteract the effect of a curved orbit and wide swath. Based on the hybrid SAR/ISAR technique, the complex-lag time-frequency distribution was exploited to refocus the maritime target images. Simulations and experiments were carried out to verify the effectiveness of the proposed method, providing precise refocusing performance in staggered mode. [ABSTRACT FROM AUTHOR]

High-resolution wide-swath (HRWS) imaging is the research focus of the modern spaceborne synthetic-aperture radar (SAR) imaging field, with significant relevance and vast application potential. Staggered SAR, as an innovative imaging system, mitigates blind areas across the entire swath by periodically altering the radar pulse repetition interval (PRI), thereby extending the swath width to multiples of that achievable by conventional systems. However, the staggered mode introduces inherent challenges, such as nonuniform azimuth sampling and echo data loss, leading to azimuth ambiguities and substantially impacting image quality. This paper proposes a sparse SAR imaging method for the low-oversampled staggered mode via compound regularization. The proposed method not only effectively suppresses azimuth ambiguities arising from nonuniform sampling without necessitating the restoration of missing echo data, but also incorporates total variation (TV) regularization into the sparse reconstruction model. This enhances the accurate reconstruction of distributed targets within the scene. The efficacy of the proposed method is substantiated through simulations and real data experiments from spaceborne missions. [ABSTRACT FROM AUTHOR]

The nonuniform sampling and reconstruction of bandlimited random signals in the SAFT domain is discussed in the paper, where the nonuniform samples are obtained by randomly disturbing the uniform sampling. First, we prove that the concerned nonuniform problem is equivalent to the process of uniform sampling after a prefilter in the statistic sense. Then, an approximate reconstruction method based on sinc interpolation is proposed for the randomized nonuniform sampling of SAFT-bandlimited random signals. Finally, we offer the mean square error estimate for the corresponding approximate recovery approach. The results generalize the conclusions of nonuniform sampling of bandlimited random signals in the FrFT and LCT domains to the SAFT domain. [ABSTRACT FROM AUTHOR]

Based on forwards recursive input–output data clustering, a recursive least squares (RLS) algorithm is proposed to estimate nonuniformly sampled nonlinear systems. The relationship of linear and nonlinear systems is studied under nonuniform sampling, and a fuzzy model is constructed for the global system. Forwards recursive input–output data clustering based on k-means clustering is used to identify the fuzzy rule number and the antecedent parameters. Based on the membership function, the consequent parameters are identified by an RLS algorithm. A practical application verified the efficiency of the method. [ABSTRACT FROM AUTHOR]

In this paper, combining the non-decaying properties with the mixed-norm properties, the revelent sampling problems are studied under the target space of L p → , 1 ω (R d) . Firstly, we will give a stability theorem for the shift-invariant subspace V p → , 1 ω (φ) . Secondly, an ideal sampling in W p → , 1 ω s (R d) is proved, and thirdly, a convergence theorem (or algorithm) is shown for V p → , 1 ω (φ) . It should be pointed out that the auxiliary function φ enjoys the membership in a Wiener amalgam space. [ABSTRACT FROM AUTHOR]

In this paper, combining the non-decaying properties with the mixed-norm properties, the revelent sampling problems are studied under the target space of L p → , 1 ω (R d) . Firstly, we will give a stability theorem for the shift-invariant subspace V p → , 1 ω (φ) . Secondly, an ideal sampling in W p → , 1 ω s (R d) is proved, and thirdly, a convergence theorem (or algorithm) is shown for V p → , 1 ω (φ) . It should be pointed out that the auxiliary function φ enjoys the membership in a Wiener amalgam space. [ABSTRACT FROM AUTHOR]

The nonuniform distribution of interference spectrum in wavenumber k-space is a key issue to limit the imaging quality of Fourier-domain optical coherence tomography (FD-OCT). At present, the reconstruction quality at different depths among a variety of processing methods in k-space is still uncertain. Using simulated and experimental interference spectra at different depths, the effects of common six processing methods including uniform resampling (linear interpolation (LI), cubic spline interpolation (CSI), time-domain interpolation (TDI), and K-B window convolution) and nonuniform sampling direct-reconstruction (Lomb periodogram (LP) and nonuniform discrete Fourier transform (NDFT)) on the reconstruction quality of FD-OCT were quantitatively analyzed and compared in this work. The results obtained by using simulated and experimental data were coincident. From the experimental results, the averaged peak intensity, axial resolution, and signal-to-noise ratio (SNR) of NDFT at depth from 0.5 to 3.0 mm were improved by about 1.9 dB, 1.4 times, and 11.8 dB, respectively, compared to the averaged indices of all the uniform resampling methods at all depths. Similarly, the improvements of the above three indices of LP were 2.0 dB, 1.4 times, and 11.7 dB, respectively. The analysis method and the results obtained in this work are helpful to select an appropriate processing method in k-space, so as to improve the imaging quality of FD-OCT. [ABSTRACT FROM AUTHOR]

A continuing priority is to better understand and resolve the barriers to using nonuniform sampling (NUS) in challenging small molecule 2D NMR with subsampling of the Nyquist grid (a.k.a. coverage) below 50%. Possible causes for artifacts, often termed sampling noise, in 1D‐NUS of 2D‐NMR are revisited here, where weak aliasing artifacts are a growing concern as NUS becomes sparser. As NUS schedules become sparser, repeat sequences are shown to occur in the dense sampling regions early in the sampling schedule, causing aliasing artifacts in resulting spectra. An intuitive screening approach that detects patterns in sampling schedules based on a convolutional filter was implemented. Sampling schedules that have low proportions of repeat sequences show significantly reduced artifacts. Another route to remediate early repeat sequences is a short period of uniform sampling at the beginning of the schedule, which also leads to a significant suppression of unwanted sampling noise. Combining the repeat sequence filter with a survey of HSQC and LR‐HSQMBC experiments, it is shown that very short initial uniform regions of about 2%–4% of the sampling space can ameliorate repeat sequences in sparser NUS and lead to robust spectral reconstructions by iterative soft thresholding (IST), even when the point spread function is unchanged. Using the principles developed here, a suite of 'one‐click' schedules was developed for broader use. [ABSTRACT FROM AUTHOR]

We consider the charge collection efficiency (CCE) for semiconductors in which the charge transport parameters, the drift mobility μ, and the carrier lifetime τ have spatial dependence, i.e., μ = μ(x) and τ = τ(x), where x is the distance from the radiation receiving top electrode toward the rear electrode. The small signal carrier packet drift analysis (CPDA) is re-examined, and the CCE efficiency for electrons and holes is formulated in terms of μ(x)τ(x)F(x), where F is the field. We use two model mobility and lifetime variations that are linear and exponential and then calculate and compare CCE determined from the CPDA equation, numerical solution of the continuity equation and Monte Carlo simulations as a function of the parameters characterizing the linear and exponential changes. The use of standard CCE equations for nonuniform samples is extensively examined, and errors are quantified by introducing a spatial average (SA) ⟨τ(x)⟩, average inverse (AI) ⟨1/τ(x)⟩, a new effective lifetime, and a kth order average. The SA lifetime works best when τ(x) monotonically decreases with x and AI works best when τ(x) monotonically increases with x. Stabilized a-Se x-ray photoconductors were considered as a practical application of this work. Both hole and electron lifetimes decrease in a-Se upon x-ray irradiation. Using the empirical equations derived recently for τh(x) and τe(x) as a function of dose D(x) in the sample, the CCE for two a-Se samples corresponding to a low-end device quality and the "best" was determined as a function of applied field. [ABSTRACT FROM AUTHOR]

This paper presents the results of a laboratory study aimed at optimizing the attachment angle of a microanchor to a sand–geogrid interface under direct shear mode. Well- and poorly graded sands, together with a single configuration comprising 24 microanchors attached at angles of 0°, 30°, 45°, 60°, and 90° to the interface are considered. All samples were prepared under dry conditions at 80% relative density and tested under normal pressures of 12.5, 25, and 50 kPa using a 300 × 300 × 170-mm direct shear box. The results show that the enhancements achieved for fine uniform sand samples were greater than for equivalent well-graded nonuniform sand samples. The optimum microanchor attachment angle for maximum interaction enhancement at the interface with well-graded sand varied between 30° and 60°, whereas this angle was 45° with the fine uniform sand. Microanchors attached at 0° and 90° angles adversely affected interaction. The greatest enhancements—of 13% and 21%—were, respectively, achieved for the well- and poorly graded sand–microanchored-geogrid samples compared with normal sand–geogrid samples. These improvements are attributed to the mobilization of passive sand resistance in front of the microanchors during shearing, with sand particle size and grading, together with normal pressure, also proving to be influential factors on the interactions. Improving sand-reinforcement interactions can reduce the amount of backfill and reinforcement required, thus reducing costs. Soils are abundantly used in the construction of earth structures. To improve the bearing capacity, reduce deformation, increase stability, and the tensile characteristics of soils, various methods, including soil reinforcement using geosynthetics, are used. Geosynthetics, such as geogrids, are widely used for reinforcing embankments and slopes, for example. The behavior of reinforced soil structures is largely governed by complex interaction mechanisms that develop between the reinforcement and the fill material. Soil–geosynthetic interactions comprise: (1) soil–geogrid skin friction; (2) soil–soil shear strength in apertures; and (3) bearing resistance against transverse ribs. To develop an understanding of the interaction mechanisms, direct shear or pullout tests are usually performed. In direct shear tests, Factors (1) and (2) are dominant, with Factor (3) being dominant in pullout tests. Passive soil resistance against transverse ribs under pullout accounts for 75% to 90% of the pullout resistance, whereas in direct shear, it contributes 10% to 12% to the overall shear resistance. To increase the contribution of passive resistance in direct shear mode, researchers have investigated different methods, including the attachment of elements as anchors to the geogrid surface. Improved interaction leads to increased stability in earth structures, reduces backfill and the amount of reinforcement required, and saves costs. [ABSTRACT FROM AUTHOR]

We establish novel uniqueness results for the Gabor phase retrieval problem: if G : L 2 (R) → L 2 (R 2) denotes the Gabor transform then every f ∈ L 4 [ − c 2 , c 2 ] is determined up to a global phase by the values | G f (x , ω) | where (x , ω) are points on the lattice b − 1 Z × (2 c) − 1 Z and b > 0 is an arbitrary positive constant. This for the first time shows that compactly-supported, complex-valued functions can be uniquely reconstructed from lattice samples of their spectrogram. Moreover, by making use of recent developments related to sampling in shift-invariant spaces by Gröchenig, Romero and Stöckler, we prove analogous uniqueness results for functions in shift-invariant spaces with Gaussian generator. Generalizations to nonuniform sampling are also presented. Finally, we compare our results to the situation where the considered signals are assumed to be real-valued. [ABSTRACT FROM AUTHOR]

A perturbation theorem for regular sampling in the Paley-Wiener space, also known as the Kadec 1 / 4 -theorem, states that if { x k : k ∈ Z } is a sequence of real numbers for which L = sup k ∈ Z | x k − k | < 1 / 4 , then any entire function f ∈ L 2 (R) of exponential type at most π can be recovered from its samples { f (x k) : k ∈ Z } . Kadec-type theorems for irregular sampling in wavelet subspaces have been discussed in several papers. However, the optimal value of L is found only in the Franklin spline wavelet subspace. This paper aims to find a better bound for L in the Kadec-type theorem for wavelet subspaces along with sampling bounds. [ABSTRACT FROM AUTHOR]

A new approach to the estimation and classification of nonlinear frequency modulated (NLFM) signals is presented in the paper. These problems are crucial in electronic reconnaissance systems whose role is to indicate what signals are being received and recognized by the intercepting receiver. NLFM signals offer a variety of useful properties not available for signals with linear frequency modulation (LFM). In particular, NLFM signals can ensure the desired reduction of sidelobes of an autocorrelation (AC) function and desired power spectral density (PSD); therefore, such signals are more frequently used in modern radar and echolocation systems. Due to their nonlinear properties, the discussed signals are difficult to recognize and therefore require sophisticated methods of analysis, estimation and classification. NLFM signals with frequency content varying with time are mainly analyzed by time–frequency algorithms. However, the methods presented in the paper belong to time–chirp domain, which is relatively rarely cited in the literature. It is proposed to use polynomial approximations of nonlinear frequency and phase functions describing signals. This allows for applying the cubic phase function (CPF) as an estimator of phase polynomial coefficients. Originally, the CPF involved only third-order nonlinearities of the phase function. The extension of the CPF using nonuniform sampling is used to analyse the higher order polynomial phase. In this paper, a sixth order polynomial is considered. It is proposed to estimate the instantaneous frequency using a polynomial with coefficients calculated from the coefficients of the phase polynomial obtained by CPF. The determined coefficients also constitute the set of distinctive features for a classification task. The proposed CPF-based classification method was examined for three common NLFM signals and one LFM signal. Two types of neural network classifiers: learning vector quantization (LVQ) and multilayer perceptron (MLP) are considered for such defined classification problem. The performance of both the estimation and classification processes was analyzed using Monte Carlo simulation studies for different SNRs. The results of the simulation research revealed good estimation performance and error-free classification for the SNR range encountered in practical applications. [ABSTRACT FROM AUTHOR]

Robot path planning in 3D space is a challenging problem for its complex configuration. Sampling-based algorithms have gained great success in solving path planning problems in 3D space, but the quality of the initial path is not guaranteed and the convergence to the optimal solution is slow. To address these problems, in this article, we present a novel sampling-based path planning framework enhanced by the deep neural network (DNN) with applications to 3D space. In the proposed framework, we first train the DNN with a number of successful path planning cases in 3D space. Then the DNN is utilized to predict the promising region where the feasible path probably exists for a given path planning problem. This predicted promising region serves as a nonuniform sampling heuristic to bias the sampling process of the path planner. In this way, the path planner can focus on the promising region in the exploration and exploitation process so that the path planning speed gets accelerated. We conduct numerical simulations to evaluate the performance of the proposed algorithm and the results show that it can perform much better than conventional path planning algorithms. Furthermore, we also investigate the performance of different DNN architectures for path planning in 3D space. Note to Practitioners—In this work, we aim to provide an efficient learning-based method to accelerate the robot path planning process in 3D space. Conventional path planning algorithms need to perceive the environment first, and then implement a series of calculations such as collision checking and data storing to generate a feasible path. When facing complex and high-dimensional environments, they do not perform well. But the proposed neural network method in this article can predict the promising region where the feasible path exists for any given environment. This prediction result is used to guide the path planning process so that the algorithm performance can get significantly improved. Apart from sampling-based algorithms, the proposed neural network model can also be extended to other types of path planning algorithms. [ABSTRACT FROM AUTHOR]

We study the sampling problem involving derivatives in periodic shift-invariant spaces. We provide a necessary and sufficient condition for periodic nonuniform stable sampling with derivatives, based on block circulant matrices. Additionally, we derive an iterative algorithm to reconstruct a function from its irregular samples involving derivatives. [ABSTRACT FROM AUTHOR]

To investigate forest resources, it is necessary to identify the tree species. However, it is a challenge to identify tree species using 3D point clouds of trees collected by light detection and ranging (LiDAR). PointNet++, a point cloud deep learning network, can effectively classify 3D objects. It is important to establish high-quality individual tree point cloud datasets when applying PointNet++ to identifying tree species. However, there are different data processing methods to produce sample datasets, and the processes are tedious. In this study, we suggest how to select the appropriate method by designing comparative experiments. We used the backpack laser scanning (BLS) system to collect point cloud data for a total of eight tree species in three regions. We explored the effect of tree height on the classification accuracy of tree species by using different point cloud normalization methods and analyzed the effect of leaf point clouds on classification accuracy by separating the leaves and wood of individual tree point clouds. Five downsampling methods were used: farthest point sampling (FPS), K-means, random, grid average sampling, and nonuniform grid sampling (NGS). Data with different sampling points were designed for the experiments. The results show that the tree height feature is unimportant when using point cloud deep learning methods for tree species classification. For data collected in a single season, the leaf point cloud has little effect on the classification accuracy. The two suitable point cloud downsampling methods we screened were FPS and NGS, and the deep learning network could provide the most accurate tree species classification when the number of individual tree point clouds was in the range of 2048–5120. Our study further illustrates that point-based end-to-end deep learning methods can be used to classify tree species and identify individual tree point clouds. Combined with the low-cost and high-efficiency BLS system, it can effectively improve the efficiency of forest resource surveys. [ABSTRACT FROM AUTHOR]

Proper field sampling strategies are important in antenna measurements and diagnostics applications to reduce the overall testing time. We investigate the role of source dimension in determining sampling points’ locations by referring to circumference geometries. An inverse problem approach is adopted, and spectral decomposition of the relevant operator is considered for a 2-D geometry. First, we introduce and discuss an approximation of the resulting point spread functions (PSFs), on which we found our approach. Next, a numerical strategy to discretize the field observation domain is presented, which results in a nonuniform angular step depending, in turn, on source extension. Some numerical examples of source characterization show the effectiveness of the approach in comparison to uniform angular sampling. [ABSTRACT FROM AUTHOR]

We introduce a new concept of variable bandwidth that is based on the frequency truncation of Wilson expansions. For this model we derive sampling theorems, a complete reconstruction of f from its samples, and necessary density conditions for sampling. Numerical simulations support the interpretation of this model of variable bandwidth. In particular, chirps, as they arise in the description of gravitational waves, can be modeled in a space of variable bandwidth. [ABSTRACT FROM AUTHOR]

Currently, backward projection (BP) imaging is widely used in different kinds of through-wall radars. This imaging method is used to make the pixel points corresponding to each echo signal consistent in the time domain by compensating for the time delay of information between the transceiver antenna and the detection target and performing coherent superposition to finally project the target in space. Because of this property, the BP imaging algorithm is computationally intense and has a long computation time, which limits its application in practical engineering. In this paper, we propose backward projection imaging of wall-penetrating radar with nonuniform sampling in the air domain to address the problem of the imaging speed of wall penetrating radar. This is a universal optimization algorithm that optimizes the imaging process of radar in scenes with sparse targets to obtain better imaging results in less time. A stepped-frequency continuous waveform (SFCW) ultra-wideband (UWB) multiple-input multiple-output (MIMO) radar is prepared for the experiments, and the imaging time of the algorithm is verified using real-world data. The results show that the method can achieve real-time imaging based on existing technology, laying a firm foundation for the practical application of through-wall radar. [ABSTRACT FROM AUTHOR]

As an innovative concept of high-resolution and wide-swath system, the low-oversampled staggered synthetic aperture radar (SAR) can not only deal with the blind ranges but also suppress range ambiguities and reduce the data volume. Due to the variation of pulse repetition interval (PRI), there will be echo pulse loss and nonuniform sampling in azimuth. Generally, the existing reconstruction algorithms mostly resample the nonuniformly sampled signal into a uniform grid and then perform conventional focused processing. However, the accuracy of the resampling is limited, and the advantage of the nonuniformity over uniform sampling in terms of reconstruction performance is ignored, especially with low oversampling factors. In this article, a reconstruction algorithm for low-oversampled staggered SAR is proposed based on the sparsity Bayesian learning (SBL) in the presence of a nonlinear PRI variation strategy. To ensure that the blind range distribution, which depends on the PRI variation strategy, brings a superior reconstruction performance, we define a novel objective function and optimize a sequence of nonlinear PRI variation with genetic algorithm (GA). On the basis of the optimized sequence, the proposed reconstruction algorithm performs the second-order keystone transform to achieve range curvature correction for nonuniformly sampled data in azimuth. Then, a nonuniform observation model is established. The SBL using a hierarchical form of the Laplace prior is applied to reconstruct the focused images directly with the nonuniform sampling. Simulations and experiments on raw data generated in the staggered SAR mode with low oversampling factors are performed to verify the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In a recent study, a 2-D pseudospectral time-domain (PSTD) full-wave simulator was developed and demonstrated to be capable of efficiently solving large-scale low-frequency (e.g., HF) electromagnetic scattering problems, for example, on the application of radar sounding simulations of planetary clutter and subsurfaces. In this article, the 2-D PSTD simulator is applied to simulate a domain as large as 4000 $\lambda $ (along-track) $\times 1666.67\,\,\lambda $ (cross-track) $\times 33.33\,\,\lambda $ (depth) with $\lambda =15$ m at an HF frequency of 20 MHz. To accomplish the goal, the simulator is further improved to efficiently model/simulate large cross-track slices of dielectric scenes by allowing nonuniform grid sampling in horizontal (lateral) and vertical directions, and the cross-track results are then stitched together along the track to form the simulated radargram. By combining the SHAllow RADar (SHARAD) viewing geometry and Mars Orbital Laser Altimeter (MOLA) digital elevation model (DEM), we simulate SHARAD returns at three different sites on Mars: one at the North Pole and two at Oxia Planum. At all three sites, the PSTD simulated radargrams are compared with measured SHARAD radargrams. Through power-level calibration and reference time adjustment, the PSTD simulated power estimates are further validated by comparing with real power observations from SHARAD with a 5-dB uncertainty and Pearson correlation coefficient of 0.3–0.4 (a $p$ -value on the order of $10^{-9}$), which justifies the use of the 2-D PSTD simulator for emulating surface clutter in planetary radar sounding. This simulator is open source and can be easily modified to support radar sounding simulations in support of other planetary missions with radar sounding instruments. [ABSTRACT FROM AUTHOR]

In this paper, two different timing-mismatch compensation strategies for two-channel time-interleaved analog-to-digital converters are comprehensively analyzed and compared. In the first strategy (SA), one channel serves as a reference channel, and the other channel is compensated to match the reference channel using the timing mismatch between the channels. In the second strategy (SB), both channels are compensated to match each other, using half the value of the channel mismatch with different signs. For SB, the paper introduces a novel compensation structure that utilizes parallel differentiator-multiplier (PDM) branches. Expressions for the spurious-free dynamic range (SFDR) after compensation are derived for both strategies. These expressions reveal that the novel PDM structure achieves a remarkably greater SFDR than the existing cascaded differentiator-multiplier (CDM) compensation structure which can be used for both SA and SB. This is because, after compensation, the remaining aliasing distortion in the proposed PDM structure is shown to be of higher approximation order (in terms of the mismatch value) and thus substantially smaller than in the CDM structure. Simulations included in the paper validate the theoretical results. [ABSTRACT FROM AUTHOR]

This paper explores fractional spectra of signals after two types of nonuniform samplings in the presence of timing offset. Both cases of bandlimited and multiband signals in the fractional Fourier domain are considered, based on which we provide conditions for reconstructing the spectrum and devise relevant methods for compensating the bias introduced by timing offset. To obtain these goals, we divide the nonuniformly sampled signal into uniformly sampled sub-sequences and establish the relationship between the discrete-time fractional Fourier transforms (DTFrFTs) of them and the FrFT of the original signal. It indicates that the obtained DTFrFTs consists of periodic replicas of the FrFT for the original signal with each replica being biased by a phase term introduced by timing offset. Based on the matrix form of the relationship, we implement spectral reconstruction of bandlimited signals under certain conditions by performing the inverse of a matrix determined by the phase terms. Different from bandlimited signals, the DTFrFTs of uniformly sampled sub-sequences for multiband signals are studied within disjoint fractional frequency sub-intervals separated by aliasing boundaries. Moreover, inverse of a matrix with fewer columns and rows is utilized to reconstruct the spectrum. Simulations verify the effectiveness of the proposed methods. • The effect of timing offset in multicoset sampling has been studied in terms of FrFT. • New methods for spectrum analysis have been devised in the presence of timing offset. • The proposed methods have low computational complexity and high accuracy. [ABSTRACT FROM AUTHOR]

Retransmission interference in radar and communication signal processing significantly threatens the received linear frequency modulation signal. With the advancement in the hardware capabilities of interference devices, they can intercept and retransmit signals within the duration of a single pulse. Therefore, we refer to this type of interference as intra-pulse retransmission interference, which includes retransmission modes smeared spectrum, interrupted sampling repeater jamming, and interrupted nonuniform sampling repeater jamming. Although traditional interference cancellation techniques offer optimal solutions under the assumption of fully known interference parameters, practical scenarios often involve unknown parameters, estimation errors, random parameters, and multiple interferences, leading to performance degradation. To address these problems, we propose a Multi-Residual Encoder-Decoder Network (MRDENet), a novel approach for effectively mitigating intra-pulse retransmission interferences and recovering the signal of linear frequency modulation. In contrast to parameter estimation and interference cancellation, MREDNet extracts crucial features of both the target and interference and performs reconstruction. More specifically, MREDNet acquires information about the retransmission pattern of interference and the modulation frequency through its multi-level residual shortcut connections. To address the issue of network parameters being real while the signals are complex, we devised decomplexification—a data preprocessing approach enabling neural networks for direct utilization in front-end complex signal processing. Besides, we evaluate the performance of MREDNet comprehensively. The experimental conditions encompassed single and multiple interferences, incomplete data sets, varying signal-to-noise ratios, and jamming-to-signal ratios. The computational simulations demonstrate that MREDNet successfully solves the problem of recovering linear frequency modulation signals interfered with by intra-pulse retransmission interference. According to the boundary condition of MREDNet, the proposed method exhibits valuable applications in real-world scenarios. • We propose a recovery network named MREDNet, which is employed for recovering LFM signals interfered by intra-pulse retransmission interference. • In contrast to other methods, MREDNet possesses the capability to batch-process multiple pulses and handle multiple interferences. • MREDNet is applicable in scenarios with varying interference types between the test and training data sets. • Simulations demonstrate that MREDNet still performs well even under conditions of high signal-to-interference ratios and low signal-to-noise ratios. [ABSTRACT FROM AUTHOR]

With the recent advancement of products pipelines digitization, a large number of sensors have been installed in pumping stations for real-time flow parameters measurement. In these asynchronous multi-sensor systems, data missing and false data attacks are likely to occur when performing online operation monitoring of the oil pipeline system. In this paper, a hybrid state estimation method is proposed to process both the missing and fault measurement, considering the dynamic operation process of the whole system. Combing frequency-domain analysis method with model-free adaptive control algorithm, the state estimation model with adaptive deviation compensation is established to characterize the nonlinear transient flow process of the pumping station. And the Kalman Filter method is adopted to overcome the interference of sensor noise. In terms of multi-rate observation data processing, this study innovatively proposes an algorithm based on the first principle and generalized predictive control theory to improve the accuracy of traditional missing data processing methods based on statistical analysis. Moreover, non-obvious abnormal observations are identified by introducing long short-term memory network characterized by deviations between sensor measurements and multi-rate state estimation results. To verify the effectiveness of proposed method, it is adopted to the unsteady state estimation of a refined oil pumping station system under the attack of noise, nonuniform asynchronous sampling and insignificant abnormal data. • A hybrid state estiamtion method for refined oil pumping stations with missing and fault measurement. • Linearized adaptive model for dynamic state estimation of nonlinaer refined oil pumping stations. • Multi-rate estimation based on GPC method for handling random missing observations. • Intergating data-driven and model-driven method for inconspicuously bad data identification. [ABSTRACT FROM AUTHOR]

• Nonuniform spatial sampling and polynomial misfits introduce aliasing and artifacts in ionospheric perturbations obtained using GPS. • Spatio-Periodic Leveling Algorithm (SPLA) is efficient in removing such aliasing and artifacts. • SPLA detects 50% more perturbations compare to conventional methods and increases SNR up to 149%. • SPLA efficiently detects perturbations at low elevations and removes the need of elevation cut-off. Ionospheric perturbations induced by tsunamis and earthquakes can be used for tsunami early warning and remote sensing of earthquakes, provided the perturbations are characterized properly to distinguish them from the ones caused by other sources. The ionospheric perturbations are increasingly being obtained from Global Positioning System (GPS) based Total Electron Content (TEC) measurements sampled at uniform time intervals. However, the sampling is not uniform in space. The nonuniform spatial sampling along the GPS satellite tracks introduces aliasing if it is not accounted while computing the ionospheric perturbations. All the methods hitherto used to detect the co-seismic and tsunamigenic ionospheric perturbations did not account the nonuniform spatial sampling while computing these perturbations. In addition, the residual approach used to obtain the perturbations by detrending the TEC time series using high-order polynomial fit introduces artifacts. These aliasing and artifacts corrupt amplitude, Signal-to-Noise Ratio (SNR), phase, and frequency of ionospheric perturbations which are vital to distinguish the perturbations induced by tsunamis and earthquakes from the rest. We show that Spatio-Periodic Leveling Algorithm (SPLA) successfully removes such aliasing and artifacts. The efficiency of SPLA in removing the aliases and artifacts is validated under two simulated scenarios, and using GPS observations carried out during two natural disasters – the 2004 Indian Ocean tsunami and the 2015 Nepal-Gorkha earthquake. We, further, studied the severity of aliasing and artifacts on co-seismic and tsunamigenic perturbations by analyzing its characteristics employing SNR, spatiotemporal, and wavelet analyses. The results reveal that removal of aliasing and artifacts using SPLA i) increases the SNR up to ∼149% compared to the residual method and ∼39% compared to the differential method, ii) distinctly resolves signals from sharp static variations, and iii) detects 50% more co-seismic ionospheric perturbations and 25% more tsunami-induced ionospheric perturbations in the two events studied. Cross-correlation of the perturbation time series obtained using the residual method and SPLA reveals that aliasing and artifacts shift the time of occurrence by −7.64 minutes to +4.21 minutes. Further, the results show that the SPLA efficiently detects the ionospheric perturbations at low elevation angles, thereby removes the need of applying elevation cut-off and increases the area of ionospheric exploration of a GPS receiver. [ABSTRACT FROM AUTHOR]

Staggered synthetic aperture radar (SAR) can effectively stagger range blind areas by periodically changing the pulse repetition interval (PRI), to achieve continuous imaging with an ultrawide swath. In conventional staggered SAR, azimuth samples are nonuniformly distributed due to the variable PRI, and complex resampling processing, such as best linear unbiased (BLU) interpolation and multichannel reconstruction processing, is required. In this article, a strict rule of PRI variation and phase center adjustment (PCA) is proposed for staggered SAR, to solve the problem of nonuniform azimuth sampling. In the proposed joint strategy of PRI variation and PCA, the relevant parameters for PCA are first determined. Then, the PRI sequence is designed according to PCA parameters to stagger blind ranges. Finally, the PCA rule is designed according to the designed PRI sequence and PCA parameters. During the data acquisition interval, the effective phase center is periodically adjusted pulse by pulse according to this rule, making the azimuth samples totally uniformly distributed. In addition, the discontinuously distributed missing samples can be estimated by signal estimation approaches. With the proposed joint rule of PRI variation and PCA, the emergence of false targets in imaging results can be avoided, and the complex resampling processing can be relieved to reduce the computational complexity. Simulation experiments on imaging results verify the advantages of this strategy. [ABSTRACT FROM AUTHOR]

Marine radar plays a significant role in ship navigation. However, when contending with interference among cosailing navigation radars, the echo data may be unintentionally corrupted, and it becomes challenging to obtain high-quality imagery using current radar imaging methods. To overcome this problem, an efficient anti-interference imaging framework is presented in this article based on the theory of nonuniform sampling. First, a beam-recursive anti-interference method based on the signal-to-interference-plus-noise ratio (SINR) estimation is proposed to compensate for the shortcoming of the traditional interference rejection method. Second, a nonuniform sampling model is established to well model the echo data with missing samples, which facilitates reconstructing the marine radar imagery from the missing echo data. Finally, a fast super-resolution method based on the dimension-reduction iterative adaptive approach (DRIAA) is proposed to reconstruct the distribution of sea-surface targets at a much lower computational complexity. Simulated and experimental results demonstrate that our anti-interference imaging framework can provide radar imagery with higher quality and lower computational complexity than the existing radar imaging methods in the presence of unintentional interference. [ABSTRACT FROM AUTHOR]

In this article, we propose a novel technique of digital predistortion (DPD) for dual-band power amplifiers (PAs) based on the periodically nonuniform sampling (PNS) theory. In contrast to conventional dual-band DPD (2-D-DPD) models, the proposed periodically nonuniform sampled DPD (PNS-DPD) has only a single input, which can largely reduce the model complexity. We fold the two stimuli with aliasing and feed them to a simple single-band DPD model. The desired predistorted signals are reconstructed from aliased DPD output through the PNS theory. Compared with conventional multi-input models that include numerous intermodulation products of the input signals, the complexity of the proposed single-input PNS-DPD model is hugely decreased. The model coefficients of the proposed PNS-DPD can be easily extracted with conventional direct or indirect learning architecture. We experimentally evaluate the proposed DPD on a test bench and compare it with other DPD techniques in the literature. The implementation complexity can be reduced by over 30%, and the identification complexity is also largely reduced. [ABSTRACT FROM AUTHOR]

Recent developments in para‐hydrogen‐induced polarization (PHIP) methods allow the nuclear magnetic resonance (NMR) detection of specific classes of compounds, down to sub‐micromolar concentration in solution. However, when dealing with complex mixtures, signal resolution requires the acquisition of 2D PHIP‐NMR spectra, which often results in long experimental times. This strongly limits the applicability of these 2D PHIP‐NMR techniques in areas in which high‐throughput analysis is required. Here, we present a combination of fast acquisition and nonuniform sampling that can afford a 10‐fold reduction in measuring time without compromising the spectral quality. This approach was tested on a mixture of substrates at micromolar concentration, for which a resolved 2D PHIP spectrum was acquired in less than 3 min. [ABSTRACT FROM AUTHOR]

Amplitude demodulation is a classical operation used in signal processing. For a long time, its effective applications in practice have been limited to narrowband signals. In this work, we generalize amplitude demodulation to wideband signals. We pose demodulation as a recovery problem of an oversampled corrupted signal and introduce special iterative schemes belonging to the family of alternating projection algorithms to solve it. Sensibly chosen structural assumptions on the demodulation outputs allow us to reveal the high inferential accuracy of the method over a rich set of relevant signals. This new approach surpasses current state-of-the-art demodulation techniques apt to wideband signals in computational efficiency by up to many orders of magnitude with no sacrifice in quality. Such performance opens the door for applications of the amplitude demodulation procedure in new contexts. In particular, the new method makes online and large-scale offline data processing feasible, including the calculation of modulator-carrier pairs in higher dimensions and poor sampling conditions, independent of the signal bandwidth. We illustrate the utility and specifics of applications of the new method in practice by using natural speech and synthetic signals. [ABSTRACT FROM AUTHOR]

State estimation is one of the main challenges in the microgrids, due to the complexity of the system dynamics and the limitations of the communication network. In this regard, a novel real-time event-based optimal state estimator is introduced in this article, which uses the proposed adaptive send-on-delta (SoD) nonuniform sampling method over wireless sensors networks. The proposed estimator requires low communication bandwidth and incurs lower computational resource cost. The threshold for the SoD sampler is made adaptive based on the average communication link delay, which is computed in a distributed form using the event-based average consensus protocol. The SoD nonuniform signal sampling approach reduces the traffic over the wireless communication network due to the events transmitted only when there is a level crossing in the measurements. The state estimator structure is extended on top of the traditional Kalman filter with the additional stages for the fusion of the received events. The error correction stage is further improved by optimal reconstruction of the signals using projection onto convex sets algorithm. Finally, an Internet of things (IoT) experimental platform based on LoRaWAN and IEEE 802.11 (WiFi) protocols are developed to analyze the performance of the state estimator for the IEEE 5 Bus case study microgrid. [ABSTRACT FROM AUTHOR]

Sampling and reconstruction of signals in a shift-invariant space are generally studied under the requirement that the generator is in a stronger Wiener amalgam space, and the error estimates are usually given in the sense of L p , 1 / ω -norm. Since we often need to reflect the local characteristics of reconstructing error, the asymptotic pointwise error estimates for nonuniform and average sampling in a non-decaying shift-invariant space are discussed under the assumption that the generator is in a hybrid-norm space. Based on Lemma 2.1–Lemma 2.6, we first rewrite the iterative reconstruction algorithms for two kinds of average sampling functionals and prove their convergence. Then, the asymptotic pointwise error estimates are presented for two algorithms under the case that the average samples are corrupted by noise. [ABSTRACT FROM AUTHOR]

Summary: The identification of the Hammerstein–Wiener (H‐W) systems based on the nonuniform input–output dataset remains a challenging problem. This article studies the identification problem of a periodically nonuniformly sampled‐data H‐W system. In addition, the product terms of the parameters in the H‐W system are inevitable. In order to solve the problem, the key‐term separation is applied and two algorithms are proposed. One is the key‐term‐based forgetting factor stochastic gradient (KT‐FFSG) algorithm based on the gradient search. The other is the key‐term‐based hierarchical forgetting factor stochastic gradient (KT‐HFFSG) algorithm. Compared with the KT‐FFSG algorithm, the KT‐HFFSG algorithm gives more accurate estimates. The simulation results indicate that the proposed algorithms are effective. [ABSTRACT FROM AUTHOR]

Conventional digital predistortion (DPD) techniques are facing the challenge of complexity in the fifth generation (5G) and beyond concurrent dual-band terminal transmitters. This article proposes novel low-complexity behavior models for the DPD of terminal power amplifiers (PAs). Derived from the conventional memory polynomial (MP) model, the new models utilize magnitude-selective affine (MSA) functions as nonlinear basis functions to greatly decrease the model complexity. The proposed paralleled envelope indexed 2-D MSA (PI-2-D-MSA) model and combined envelope indexed 2-D MSA (CI-2-D-MSA) model take both the in-band intermodulation and cross-band modulation into account and can well compensate for nonlinear distortion in dual-band terminal PAs. Moreover, the proposed models are extended to nonuniform sampling rate (NSR) scenarios, where the aliasing effect for the low sampling rate band is analyzed. Simulations and experimental measurements under the uniform sampling rate and the NSR scenarios were carried out on a 1.7–2.8-GHz wideband Doherty PA and a 4.4–5.0-GHz class-AB terminal PA and demonstrated the linearization performances of the proposed models. The total numbers of floating-point operations (FLOPs) of the PI-2-D-MSA and the CI-2-D-MSA models were 11% and 8% of that of the prior 2-D-MP model, respectively. Even though their linearization accuracy deteriorated, the relaxed linearization standard for terminal transmitters can still be achieved. [ABSTRACT FROM AUTHOR]

Modeling time series (TS) is a research focus in cryospheric sciences because of the complexity and multiscale nature of events of interest. Highly nonuniform sampling of measurements from different sensors with different levels of accuracy, as is typical for measurements of ice sheet elevations, makes the problem even more challenging. In this article, we propose a spline-based approximation framework (ALPS—Approximation by Localized Penalized Splines) for modeling TS of land ice changes. The localized support of the B-spline basis functions enable robustness to nonuniform sampling, a considerable improvement over other global and piecewise local models. With features like discrete-coordinate-difference-based penalization and two-level outlier detection, ALPS further guarantees the stability and quality of approximations. ALPS incorporates rigorous model uncertainty estimates with all approximations. As demonstrated by examples, ALPS performs well for a variety of data sets, including TS of ice sheet thickness, elevation, velocity, and terminus locations. The robust estimation of TS and their derivatives facilitates new applications, such as the reconstruction of high-resolution elevation change records by fusing sparsely sampled TS of ice sheet thickness changes with modeled firn thickness changes, and the analysis of the relationship between different outlet glacier observations to gain new insights into processes and forcing. [ABSTRACT FROM AUTHOR]

The number circled in green originally listed as a 2 as seen in the left figure, was a typo, possibly because the prior number was a 2, which was accidentally repeated. Cullen, L. E., Marchiori, A., Rovnyak, D., Magn Reson Chem 2023, 61 (9-10), 337. https://doi.org/10.1002/mrc.5340 Explanation of typo in Figure S1 panel (a) for editorial review: For comparison, the original is left and the corrected is right. Correction to "Revisiting aliasing noise to build more robust sparsity in nonuniform sampling 2D-NMR". [Extracted from the article]

Although the concepts of nonuniform sampling (NUS) and non-Fourier spectral reconstruction in multidimensional NMR began to emerge 4 decades ago (Bodenhausen and Ernst, 1981; Barna and Laue, 1987), it is only relatively recently that NUS has become more commonplace. Advantages of NUS include the ability to tailor experiments to reduce data collection time and to improve spectral quality, whether through detection of closely spaced peaks (i.e., "resolution") or peaks of weak intensity (i.e., "sensitivity"). Wider adoption of these methods is the result of improvements in computational performance, a growing abundance and flexibility of software, support from NMR spectrometer vendors, and the increased data sampling demands imposed by higher magnetic fields. However, the identification of best practices still remains a significant and unmet challenge. Unlike the discrete Fourier transform, non-Fourier methods used to reconstruct spectra from NUS data are nonlinear, depend on the complexity and nature of the signals, and lack quantitative or formal theory describing their performance. Seemingly subtle algorithmic differences may lead to significant variabilities in spectral qualities and artifacts. A community-based critical assessment of NUS challenge problems has been initiated, called the "Nonuniform Sampling Contest" (NUScon), with the objective of determining best practices for processing and analyzing NUS experiments. We address this objective by constructing challenges from NMR experiments that we inject with synthetic signals, and we process these challenges using workflows submitted by the community. In the initial rounds of NUScon our aim is to establish objective criteria for evaluating the quality of spectral reconstructions. We present here a software package for performing the quantitative analyses, and we present the results from the first two rounds of NUScon. We discuss the challenges that remain and present a roadmap for continued community-driven development with the ultimate aim of providing best practices in this rapidly evolving field. The NUScon software package and all data from evaluating the challenge problems are hosted on the NMRbox platform. [ABSTRACT FROM AUTHOR]

Blade health monitoring (BHM) is an important technology to ensure safe operation of turbine machinery. The blade tip timing (BTT) method is a non-contact approach of vibration monitoring that is widely used for aero-engines. A BTT signal can be characterized as nonuniform and sub-Nyquist sampled (i.e., under-sampled). For nonuniform sampling, the least squares (LS) fitting method has long been used to reconstruct the spectrum. However, the under-sampling of the BTT signal causes the spectrum obtained by LS fitting aliasing. The iterative reweighted LS periodogram (IRLSP) can eliminate the aliasing caused by sub-Nyquist and nonuniform sampling. This method weakens the frequency aliasing through the method of reweighted iteration, but the consequence of this operation is that the amount of calculation is greatly increased. Thus, we propose an adaptive iterative approach (AIA) based on the IRLSP that combines a priori information of the blade. The main contribution of this method is to improve the computational efficiency for processing the BTT signal and the effect of anti-aliasing. These two points mean that this method is expected to become a real-time blade vibration monitoring method. We combined a finite element model with modal testing to perform simulations and verify the improvement with AIA. A large number of experiments were also performed to verify the effectiveness of our approach for BHM. [ABSTRACT FROM AUTHOR]

In this paper, we derive tail bounds for the norms of random submatrices with nonuniformly distributed supports. We apply these results to sparse approximation and conduct an analysis of the average case performance of thresholding, orthogonal matching pursuit, and basis pursuit. As an application of these results, we characterize sensing dictionaries to improve average performance in the nonuniform case and test their performance numerically. [ABSTRACT FROM AUTHOR]

In this work, large-scale multiple-antenna systems are investigated, where the base station employs a large antenna array with low-cost and low-power 1-bit analog-to-digital converters. To compensate for the performance loss caused by the coarse quantization, oversampling is applied at the receiver. Unlike existing works that use uniform oversampling, which samples the signal at a constant rate, a novel dynamic oversampling scheme is proposed. The basic idea is to perform time-varying nonuniform oversampling, which selects samples with nonuniform patterns that vary over time. We consider two system design criteria: a design that maximizes the achievable sum rate and another design that minimizes the mean square error of detected symbols. Dynamic oversampling is carried out using a dimension reduction matrix Δ, which can be computed by the generalized eigenvalue decomposition or by novel submatrix-level feature selection algorithms. Moreover, the proposed scheme is analyzed in terms of convergence, computational complexity and power consumption at the receiver. Simulations show that systems with the proposed dynamic oversampling outperform those with uniform oversampling in terms of computational cost, achievable sum rate and symbol error rate performance. [ABSTRACT FROM AUTHOR]

Nonuniform sampling (NUS) of multidimensional NMR experiments is a powerful tool to obtain high‐resolution spectra with less instrument time. With NUS, only a subset of the points needed for conventional Fourier transformation is recorded, and sophisticated algorithms are needed to reconstruct the missing data points. During the last decade, several software packages implementing the reconstruction algorithms have emerged and been refined and now result in spectra of almost similar quality as spectra from conventionally recorded and processed data. However, from the number of literature references to the reconstruction methods, many more multidimensional NMR spectra could presumably be recorded with NUS. To help researchers considering to start using NUS for their NMR experiments, we here review 13 different reconstruction methods found in five software packages (CambridgeCS, hmsIST, MddNMR, NESTA‐NMR, and SMILE). We have compared how the methods run with the provided example scripts for reconstructing a nonuniform sampled three‐dimensional 15N–NOESY–HSQC at sampling densities from 5% to 50%. Overall, the spectra are all of similar quality above 20% sampling density. Thus, without any particular knowledge about the details of the reconstruction algorithms, significant reduction in the experiment time can be achieved. Below 20% sampling density, the intensities of particular weak peaks start being affected. MddNMR's IST with virtual echo and the SMILE algorithms still reproduced the spectra with the highest accuracy of peak intensities. [ABSTRACT FROM AUTHOR]

Monitoring of chemical reactions is best carried out using methods that sample the test object at a rate greater than the time scale of the processes taking place. The recently proposed time‐resolved nonuniform sampling (TR‐NUS) method allows the use of two‐dimensional (2D) nuclear magnetic resonance (NMR) spectra for this purpose and provides a time resolution equivalent to that achievable using one‐dimensional spectra. Herein, we show that TR‐NUS acquired data eliminates 2D spectral line disturbances and enables more accurate signal integration and kinetics conclusions. The considerations are exemplified with a seemingly simple aza‐Michael reaction of benzylamine and acrylamide. Surprisingly, the product identification is possible only using 2D spectra, although credible monitoring requires TR‐NUS. [ABSTRACT FROM AUTHOR]

In this work, we discuss representative examples of the application of nonuniform sampling (NUS) in small‐molecule structure determination in a pharmaceutical research and development and quality control setting. We demonstrate the advantages of NUS over traditional sampling in various industrial applications of nuclear magnetic resonance (NMR). We propose an optimal trade‐off between the quality and the time efficiency of 'routine' measurements, as demonstrated via a test sample of vinpocetine analyzed on a 'work horse' NMR spectrometer. In addition, we present case studies where the application of NUS contributed significantly to the successful completion of some challenging structure determination task at hand. To that end, in some cases, we combined NUS with a method of decoupling in the indirect dimension that gives 'constant time' nuclear Overhauser effect spectroscopy (NOESY) and 'constant time' heteronuclear multiple bond correlation (HMBC) spectra. NUS proved to be superior over traditional sampling even for the analysis of trace impurities, where the need to cope with a thousand‐fold or even larger dynamic range and low signal‐to‐noise ratio for the impurity signals is quite a challenge. [ABSTRACT FROM AUTHOR]

An important step in the process of protein research by NMR is the assignment of chemical shifts. In the coat protein of IKe bacteriophage, there are 53 residues making up a long helix resulting in relatively high spectral ambiguity. Assignment thus requires the collection of a set of three‐dimensional (3D) experiments and the preparation of sparsely labeled samples. Increasing the dimensionality can facilitate fast and reliable assignment of IKe and of larger proteins. Recent progress in nonuniform sampling techniques made the application of multidimensional NMR solid‐state experiments beyond 3D more practical. 4D 1H‐detected experiments have been demonstrated in high‐fields and at spinning speeds of 60 kHz and higher but are not practical at spinning speeds of 10–20 kHz for fully protonated proteins. Here, we demonstrate the applicability of a nonuniformly sampled 4D 13C/15N‐only correlation experiment performed at a moderate field of 14.1 T, which can incorporate sufficiently long acquisition periods in all dimensions. We show how a single CANCOCX experiment, supported by several 2D carbon‐based correlation experiments, is utilized for the assignment of heteronuclei in the coat protein of the IKe bacteriophage. One sparsely labeled sample was used to validate sidechain assignment of several hydrophobic‐residue sidechains. A comparison to solution NMR studies of isolated IKe coat proteins embedded in micelles points to key residues involved in structural rearrangement of the capsid upon assembly of the virus. The benefits of 4D to a quicker assignment are discussed, and the method may prove useful for studying proteins at relatively low fields. [ABSTRACT FROM AUTHOR]