Sampling Function Research Articles

Improvement of Computational Efficiency for Fast ISAR Image Simulation Through Nonuniform Fast Fourier Transform

The image-domain ray-tube integration formula (IRIF) is an efficient way to build a large database for synthetic-aperture radar automatic target recognition (SAR-ATR) because the IRIF can rapidly generate an ISAR image of a computer-aided design (CAD) model. Additionally, calculation of the IRIF can be accelerated by a nonuniformly sampled impulse train and the nonuniform fast Fourier transform (NUFFT). In a numerical implementation, upsampled ISAR images are required and the IRIF can calculate the upsampled ISAR images directly in image-domain. However, image-domain upsampling increases the computation time because the NUFFT calculates a matrix whose size is increased by the upsampling factor. In this letter, we propose a method to minimize the increase in computation time caused by image-domain upsampling. We derive a formula to approximately predict the scattered far-field under the small-angle condition and accelerate the formula by utilizing the nonuniformly sampled impulse train and the NUFFT. The NUFFT is used to calculate a far-field matrix without upsampling. Then, zero-padding in the field-domain and the FFT are utilized to generate an upsampled ISAR image. To validate the proposed method, ISAR images of a tank and a helicopter CAD models were simulated and were compared with those of the previous methods.

The Talbot effect as the fundamental solution to the free Schrödinger equation

The Talbot effect is usually modeled using the Helmholtz equation, but its main experimental features are captured by the solution to the free Schrödinger equation with the Dirac comb as initial datum. This simplified description is a consequence of the paraxial approximation in geometric optics. However, it is a heuristic approximation that is not mathematically well justified, so K. I. Oskolkov raised in [20] the problem of ‘‘mathematizing’’ it. We show that it holds exactly in the sense of distributions.

Swell-Triggered Seismicity at the Near-Front Damage Zone of the Ross Ice Shelf

Abstract Ocean swell interacting with Antarctic ice shelves produces sustained (approximately, 2×106 cycles per year) gravity-elastic perturbations with deformation amplitudes near the ice front as large as tens to hundreds of nanostrain. This process is the most energetically excited during the austral summer, when sea ice-induced swell attenuation is at a minimum. A 2014–2017 deployment of broadband seismographs on the Ross Ice shelf, which included three stations sited, approximately, 2 km from the ice front, reveals prolific swell-associated triggering of discrete near-ice-front (magnitude≲0) seismic subevents, for which we identify three generic types. During some strong swell episodes, subevent timing becomes sufficiently phase-locked with swell excitation, to create prominent harmonic features in spectra calculated across sufficiently lengthy time windows via a Dirac comb effect, for which we articulate a theoretical development for randomized interevent times. These events are observable at near-front stations, have dominant frequency content between 0.5 and 20 Hz, and, in many cases, show highly repetitive waveforms. Matched filtering detection and analysis shows that events occur at a low-background rate during all swell states, but become particularly strongly excited during large amplitude swell at rates of up to many thousands per day. The superimposed elastic energy from swell-triggered sources illuminates the shelf interior as extensional (elastic plate) Lamb waves that are observable more than 100 km from the ice edge. Seismic swarms show threshold excitation and hysteresis with respect to rising and falling swell excitation. This behavior is consistent with repeated seismogenic fracture excitation and growth within a near-ice-front damage zone, encompassing fracture features seen in satellite imagery. A much smaller population of distinctly larger near-front seismic events, previously noted to be weakly associated with extended periods of swell perturbation, likely indicate calving or other larger-scale ice failures near the shelf front.

Dorsal root ganglion stimulation of injured sensory neurons in rats rapidly eliminates their spontaneous activity and relieves spontaneous pain.

Dorsal root ganglion field stimulation (GFS) relieves evoked and spontaneous neuropathic pain by use-dependent blockade of impulse trains through the sensory neuron T-junction, which becomes complete within less than 1 minute for C-type units, also with partial blockade of Aδ units. We used this tool in the spinal nerve ligation (SNL) rat model to selectively block sensory neuron spontaneous activity (SA) of axotomized neurons at the fifth lumbar (L5) level vs blockade of units at the L4 level that remain uninjured but exposed to inflammation. In vivo dorsal root single-unit recordings after SNL showed increased SA in L5 units but not L4 units. Ganglion field stimulation blocked this SA. Ganglion field stimulation delivered at the L5 dorsal root ganglion blocked mechanical hyperalgesia behavior, mechanical allodynia, and ongoing spontaneous pain indicated by conditioned place preference, whereas GFS at L4 blocked evoked pain behavior but not spontaneous pain. In vivo single-unit recordings of spinal cord dorsal horn (DH) wide-dynamic-range neurons showed elevated SA after SNL, which was reduced by GFS at the L5 level but not by GFS at the L4 level. In addition, L5 GFS, but not L4 GFS, increased mechanical threshold of DH units during cutaneous mechanical stimulation, while L5 GFS exceeded L4 GFS in reducing evoked firing rates. Our results indicate that SA in injured neurons supports increased firing of DH wide-dynamic-range neurons, contributing to hyperalgesia, allodynia, and ongoing pain. Ganglion field stimulation analgesic effects after nerve injury are at least partly attributable to blocking propagation of this SA.

Eberlein decomposition for PV inflation systems

The Dirac combs of primitive Pisot–Vijayaraghavan (PV) inflations on the real line or, more generally, in {mathbb {R}}^d are analysed. We construct a mean-orthogonal splitting for such Dirac combs that leads to the classic Eberlein decomposition on the level of the pair correlation measures, and thus to the separation of pure point versus continuous spectral components in the corresponding diffraction measures. This is illustrated with two guiding examples, and an extension to more general systems with randomness is outlined.

Relations of Time-Varying Circuit Parameters and Idlerless Parametric Harmonic Generation for Reconfigurable Frequency Multipliers

The idlerless relations between parametric harmonic generation and time-varying circuit parameters, such as elastance ( S), capacitance ( C), conductance ( G), and resistance ( R), are described in this work. It is shown that the time-varying response of the S, C, G, or R parameter is periodic with N-1 periods over one sinusoidal pumping cycle for N- times multiplication in idlerless reactive and resistive parametric multipliers. Under sinusoidal pumping and with the N-1 periods of the time-varying response described by Chebyshev polynomials of the first kind, the generation of odd- and even-order harmonics is realized. An approach of representing a transient train of impulses under sinusoidal pumping is also described to model the resistive multipliers. The minimum conversion loss (CL) and the maximum conversion efficiency of parametric multipliers are derived. It is shown that, at high relative frequencies, the proposed time-varying response is theoretically capable of achieving higher maximum efficiency than what is calculated with conventional idler-based multipliers. A millimeter-wave (mm-wave) switched-capacitor varactor (SCV) with tunable capacitance-voltage curves is utilized to build third-, fourth-, and fifth-order D-band reconfigurable frequency multipliers (RFMs). The simulations and measurements demonstrate the validity of the proposed theory of the tunable parametric harmonic generation. The relative bandwidths of the D-band RFM are 38.8%, 35.4%, and 25.5% with the output power at -26.6, -37.2, and -40.5 dBm for three-, four-, and five-times multiplications, respectively. An example of a D-band resistive multiplier with a tunable nonlinearity is also given.

The relation between the effective band mass in a solid and the free electron mass

The Kronig–Penney model is a model used to study properties of electrons confined in a periodic potential. It is a useful model since the electronic properties can be studied analytically with the aid of Bloch’s theorem. An important concept that emerges from the resultant electron band theory is the electron effective mass. Through the use of the Kronig–Penney model we use the so-called ‘effective mass theorem’, that allows us to ask and answer the question of how the electron effective mass depends on both the free electron mass and the characteristics of the periodic potential. We illustrate the crossover from the case of a weak periodic potential to a strong periodic potential using this theorem and explicit calculations with the Kronig–Penney model. The special case of the Dirac comb model is also treated in this work. Through the use of the ‘effective mass theorem’, we show, among other properties, that an electron–hole effective mass asymmetry is generally expected, even without considering contributions from electron–electron interactions.

Structural response of corrugated plates under blast loading: The influence of the pressure-time history

The propagation of shock waves in confined environments is a complex phenomenon due to the potential for a multiplicity of reflections, diffraction and superposition of waves. The study of such wave propagation effects, which is different from the propagation of shock waves in free-field scenarios, is not entirely described in literature, especially when studying their influence on the response of structures. The analysis of such phenomena is of extreme relevance to the evaluation of protective structures to ensure the security of equipment and personnel. This paper studies the influence of shock wave related parameters on the mechanical response of simple structural elements. This is achieved through the analysis of the impulse train, multiple positive and negative pressure profiles and signal simplifications. This research uses the finite element code LS-DYNA to analyse the structural response sensitivity of a metallic plate to different parameters, when subjected to pressure data recorded from experimental tests. It is observed that the structural response is significantly influenced by the loading regime. Results indicate that the impulse has a significant effect on the deflection-time history of the structure in the impulsive regime and that the peak pressure and pulse duration affect the deflection response in the dynamic regime. It also shows that correctly defining the negative impulse train in the pressure-time history is one of the main factors leading to an accurate modelling of the mechanical response of the structure. It is also found that a complex and realistic pressure history profile can be reduced to a simplified pulse for structural analysis and design purposes.

Spectrum Aliasing Does not Occur in Case of Ideal Signal Sampling

A new model of ideal signal sampling operation is developed in this paper. This model does not use the Dirac comb in an analytical description of sampled signals in the continuous time domain. Instead, it utilizes functions of a continuous time variable, which are introduced in this paper: a basic Kronecker time function and a Kronecker comb (that exploits the first of them). But, a basic principle behind this model remains the same; that is it also a multiplier which multiplies a signal of a continuous time by a comb. Using a concept of a signal object (or utilizing equivalent arguments) presented elsewhere, it has been possible to find a correct expression describing the spectrum of a sampled signal so modelled. Moreover, the analysis of this expression showed that aliases and folding effects cannot occur in the sampled signal spectrum, provided that the signal sampling is performed ideally.

A Simplified Analytical Solution of Mechanical Responses of Soil Subjected to Repeated Impact Loading

A simplified dynamic response model is proposed based on the deformation and dynamic stress response characteristics of soil under impact loading. The foundation is divided into two distinct zones: a projection cylinder acting vertically under impact loading and a hollow cylinder outside the projection area. It is assumed that the ramming deformation of the projected cylinder under the vertical impact load is a quasi-static loading process under the maximum contact dynamic stress through the quasi-static method, and the settlement calculation without lateral deformation is given. It is assumed that the inner wall of the hollow cylinder is subjected to horizontal lateral pressure and the analytical solution of the horizontal dynamic stress considering the plastic deformation of soil is given. The simplified dynamic response model can reflect the mechanical response of soil under impulse train load well which can provide reference for similar projects.

Relationship between electron flux and electron complexity in a disordered Dirac comb

The transfer matrix method is used to calculate the electronic states of a finite chain of structurally disordered delta-function potentials. With the probability density for the electrons in the chain we calculate a complexity measure C for a continuous probability distribution, defined by a function of Shannon’s entropy H, as an order measure of the chain, and the inverse participation ratio, or disequilibrium D, as a measure of localization of electron states. C is minimal for a completely ordered and maximal for a completely disordered chain. It is used as an indicator for the electronic transport in disordered systems characterized by a disorder parameter W. We also compare C with the transmission coefficient, T, and the inverse participation ratio D. A statistical interpretation is formulated based on the relationship between the disorder in the delta-function potentials and the transmitted and reflected electron flux. Hence, we are able to interpret the behavior of C with the formation of localized Gaussian distribution of the transmitted and reflected electron current j for growing disorder W.

Sensitivity of the surrogate analysis method to synchronization and conduction velocity of muscular fibers

This paper shows that conduction velocity (CV) and motor unit action potential (MUAPs) synchronization affects the results of Surrogate Analysis (SA) of the surface electromyography (sEMG) signal. It will be verified if the SA can extract information from the sEMG signal. Also, it is the first time that the SA is interpreted from a physiological point-of-view. To illustrate the relationships between the CV, the synchronization and the SA, a simple dipole-based model for (sEMG) signal simulation is used. It is composed of multiple fibers superposed at the same location, leaving aside any complex geometrical considerations, but putting the emphasis on the timing of the MUAPs firing. Single-pulse synchronization as well as impulse train synchronization are studied. To highlight the difference between spectral (linear) features, nonlinear features and SA relation with the model parameters, the Median Frequency (MDF), the Kurtosis, the Higuchi’s Fractal Dimension (FD) and the FD based SA are compared. The simulation results show that the SA is jointly influenced by CV and the MUAPs synchronization, almost in a multiplicative way. These relations are also more pronounced for an impulse train than for a single pulse. Overall, the SA is shown to be a good feature to consider for CV and MUAPs synchronization estimation. It is moreover uncorrelated with spectral features and moderately with nonlinear features. These findings can be used to 1) help evaluate the CV and MUAPs synchronization and 2) interpret the result of the surrogate analysis.

Band spectra of periodic hybrid $$\delta \text {-}\delta '$$ structures

We present a detailed study of a generalised one-dimensional Kronig-Penney model using $\delta\text{-}\delta'$ potentials. We analyse the band structure and the density of states in two situations. In the first case we consider an infinite array formed by identical $\delta\text{-}\delta'$ potentials standing at the linear lattice nodes. This case will be known throughout the paper as the one-species hybrid Dirac comb. We investigate the consequences of adding the $\delta'$ interaction to the Dirac comb by comparing the band spectra and the density of states of pure Dirac-$\delta$ combs and one-species hybrid Dirac combs. Secondly we study the quantum system that arises when the periodic potential is the one obtained from the superposition of two one-species hybrid Dirac combs displaced one with respect to the other and with different couplings. The latter will be known as the two-species hybrid Dirac comb. One of the most remarkable results is the appearance of a curvature change in the band spectrum when the $\delta'$ couplings are above a critical value.

Forward-backward filtering and penalized least-Squares optimization: A Unified framework

The paper proposes a framework for unification of the penalized least-squares optimization (PLSO) and forward-backward filtering scheme. It provides a mathematical proof that forward-backward filtering (zero-phase IIR filters) can be presented as instances of PLSO. On the basis of this result, the paper then represents a unifying approach to the design and implementation of forward-backward filtering and PLSO algorithms in the time and frequency domain. A new block-wise matrix formulation is also presented for implementing the PLSO and forward-backward filtering algorithms. The approach presented in this paper is particularly suited for understanding the task of zero-phase filters in the time domain and analyzing PLSO algorithms in the frequency domain. In this paper, we show that the task of a zero-phase digital Butterworth filter in the time domain is to fit the signal with impulse train and penalties on the derivatives of the fitted model. For a zero-phase digital Chebyshev filter, a linear combination of derivatives of the model is used in the penalty term.

Gauss sums, superoscillations and the Talbot carpet

We consider the evolution, for a time-dependent Schrödinger equation, of the so-called Dirac comb. We show how this evolution allows us to recover explicitly (indeed optically) the values of the quadratic generalized Gauss sums. Moreover we use the phenomenon of superoscillatory sequences to prove that such Gauss sums can be asymptotically recovered from the values of the spectrum of any sufficiently regular function compactly supported on R. The fundamental tool we use is the so called Galilean transform that was introduced and studied in the context on non-linear time dependent Schrödinger equations. Furthermore, we utilize this tool to understand in detail the evolution of an exponential eiωx in the case of a Schrödinger equation with time-independent periodic potential.

Chaotic solitons in driven sine-Gordon model

Profiles of static solitons in one-dimensional scalar field theory satisfy the same equations as trajectories of a fictitious particle in multidimensional mechanics. We argue that the structure and properties of the solitons are essentially different if the respective mechanical motions are chaotic. This happens in multifield models and models with spatially dependent potential. We illustrate our findings using one-field sine-Gordon model in external Dirac comb potential. First, we show that the number of different "chaotic" solitons grows exponentially with their length, and the growth rate is related to the topological entropy of the mechanical system. Second, the field values of stable solitons form a fractal; we compute its box-counting dimension. Third, we demonstrate that the distribution of field values in the fractal is related to the metric entropy of the analogous mechanical system.

Analgesic dorsal root ganglionic field stimulation blocks conduction of afferent impulse trains selectively in nociceptive sensory afferents.

Increased excitability of primary sensory neurons after peripheral nerve injury may cause hyperalgesia and allodynia. Dorsal root ganglion field stimulation (GFS) is effective in relieving clinical pain associated with nerve injury and neuropathic pain in animal models. However, its mechanism has not been determined. We examined effects of GFS on transmission of action potentials (APs) from the peripheral to central processes by in vivo single-unit recording from lumbar dorsal roots in sham injured rats and rats with tibial nerve injury (TNI) in fiber types defined by conduction velocity. Transmission of APs directly generated by GFS (20 Hz) in C-type units progressively abated over 20 seconds, whereas GFS-induced Aβ activity persisted unabated, while Aδ showed an intermediate pattern. Activity generated peripherally by electrical stimulation of the sciatic nerve and punctate mechanical stimulation of the receptive field (glabrous skin) was likewise fully blocked by GFS within 20 seconds in C-type units, whereas Aβ units were minimally affected and a subpopulation of Aδ units was blocked. After TNI, the threshold to induce AP firing by punctate mechanical stimulation (von Frey) was reduced, which was reversed to normal during GFS. These results also suggest that C-type fibers, not Aβ, mainly contribute to mechanical and thermal hypersensitivity (von Frey, brush, acetone) after injury. Ganglion field stimulation produces use-dependent blocking of afferent AP trains, consistent with enhanced filtering of APs at the sensory neuron T-junction, particularly in nociceptive units.

Design Low Power Detection QPSK-Transceiver for UWB Techniques

This paper presents the implementation and investigation of the quarter phase shift keying low power detection. The receiver is designed and modeled using Matlab. It was tested for different values of SNR with a constant input signal power of 100 mW. The FFT based receiver performance is measured theoretically by transmitting 1000 information symbols from the transmitter end with 7 dB improvement at Bit Error Rate BER of 10e−4, Multi Modulation Techniques Recommended and not Recommended are simulated in this research. In this research the modulation method was selected on the basis of reducing rates of the interference in the UWB communication techniques and the essential modulation should have several types of spectrum random distribution methods to reduce the level of the interference on account of the impulse train that transmitted.

Mumford–Shah functionals on graphs and their asymptotics

We consider adaptations of the Mumford–Shah functional to graphs. These are based on discretizations of nonlocal approximations to the Mumford–Shah functional. Motivated by applications in machine learning we study the random geometric graphs associated to random samples of a measure. We establish the conditions on the graph constructions under which the minimizers of graph Mumford–Shah functionals converge to a minimizer of a continuum Mumford–Shah functional. Furthermore we explicitly identify the limiting functional. Moreover we describe an efficient algorithm for computing the approximate minimizers of the graph Mumford–Shah functional.

S149. CHANGES IN FRONTO-PARIETAL CONNECTIVITY IN SCHIZOPHRENIA: TMS AND FNIRS STUDY

BackgroundOne of the most prominent deficits in schizophrenia is impairment in executive function. This impairment is associated to aberrant function of the dorso-lateral prefrontal cortex (DLPFC)(Weinberger et al. 1986) and the fronto-parietal network (FPN) (Deserno et al. 2012). The FPN is involved in cognitive control (Seeley et al. 2007, Zanto & Gazzaley 2013). While correlations of activation of DLPFC and inferior parietal lobe (IPL) are well documented, fMRI based techniques cannot determine causal relationships of interactions between brain regions. We used Transcranial magnetic stimulation (TMS), which directly affects the stimulated brain region and connected brain areas (Valchev et al 2015) and therefore can be used to investigate causal interactions between brain regions. TMS stimulation to the DLPFC at 10 Hz may cause either putative increase or decrease of activation in the in the IPL, depending on whether connections are inhibitory or excitatory (Curtin et al 2019). We hypothesised that patients with schizophrenia would have slower reaction in IPL as a consequence of DLPFC stimulation.MethodsThirteen patients and fourteen healthy controls (HC) underwent transcranial magnetic stimulation (TMS) to the right DLPFC. TMS consisted of 20 trains of impulses at 10 Hz for 3 seconds, and 60 seconds waiting time. Simultaneously, we measured brain activation IPL using functional near infrared spectroscopy (fNIRS). Diagnostic category was confirmed using MINI plus interview. The severity of symptoms was assessed using the positive and negative syndrome scale (PANSS). We estimated levels of Oxygenised haemoglobin (HbO) using NIRSLab software. GLM was applied using both hemodynamic response function (HRF) and it’s derivative. T-test was used, with FDR correction, to compare time segments of HbO following TMS stimulation.ResultsThere was no difference in age and gender between the groups. The two groups differed in education (t(2,25)= 2,584, p=0.016). GLM revealed decreased levels of HbO in HC in bilateral IPL following the TMS to the DLPFC (p_bonferroni=0.05). However, when patients were compared to HC higher levels of HbO were observed (p=0.05). However, no difference in derivative of HRF was observed. In addition, there was a significant difference in time courses between patients and HC following TMS stimulation. Namely, while there was an immediate decrease in parietal HbO levels in HC, in SZ first an increase, followed by a decrease was observed. This was significant (at a threshold level of pFDR=0.05) for several time segments and channels in both right and left IPL.DiscussionWe observed differences in activation of bilateral IPL as a consequence of DLPFC stimulation in patients with schizophrenia. Namely, there was an initial increase in HbO levels, as opposite to HC who had an immediate decrease in HbO level. This indicates opposite function of information processing from the frontal to parietal lobe in schizophrenia patients. This is in line with the idea of impaired fronto-parietal inhibition in schizophrenia which has been proposed to underlie impairments in schizophrenia such as lack of cognitive control.