Sampling Function Research Articles

Study on Excitation Forces Generated by Defective Races of Rolling Bearing

The vibrations generated by defective rolling elements bearing play vital role in dynamics of rotating machines. In this paper different approach for simulation and numerical analysis of defective bearing races presented by researchers have been compared and extended for multiple defects. This work has been attempted to demonstrate the way of modelling and simulation of local and distributed defect on inner and outer race of deep groove ball bearing. The bearing defect has been modelled as impulse train force or impact force to cause an additional deflection or excitation of rolling elements. The simulated results have been analysed in time and frequency domain. The characteristics defect frequency and its harmonics and amplitude of vibration response of defective bearing is broadly investigated through simulated results.

Sampling and Reconstruction of Operators

We study the recovery of operators with a bandlimited Kohn–Nirenberg symbol from the action of such operators on a weighted impulse train, a procedure we refer to as sampling of operators. Kailath, Bello, and later Kozek and the authors have shown that the sampling of operators is possible if the symbol of the operator is bandlimited to a set with area less than one. In this paper, we develop the theory of the sampling of operators in analogy with the classical theory of sampling of bandlimited functions. We define the notions of sampling set and sampling rate for operators and give necessary and sufficient conditions on the sampling rate that depend on the size and geometry of the bandlimiting set. We develop explicit reconstruction formulas for operator sampling that generalize reconstruction formulas for bandlimited functions. We give necessary and sufficient conditions on the bandlimiting set under which sampling of operators is possible by their action on a given periodically weighted delta train. We show that under mild geometric conditions on the bandlimiting set, classes of operators are bandlimited to an unknown set of area less than one-half permit sampling and reconstruction. We generalize two results of the Heckel and Bolcskei concerning sampling of operators with area not greater than one-half and less than one, respectively, by finding a larger class of operators to which they apply. Operators with bandlimited symbols have been used to model doubly dispersive communication channels with slowly time-varying impulse response. The results in this paper are rooted in work by Bello and Kailath in the 1960s.

Integration of a Dirac comb and the Bernoulli polynomials

For any positive integer n, we consider the ordinary differential equations of the formy(n)=1−Ш+F where Ш denotes the Dirac comb distribution and F is a piecewise-C∞ periodic function with null average integral. We prove the existence and uniqueness of periodic solutions of maximal regularity. Above all, these solutions are given by means of finite explicit formulae involving a minimal number of Bernoulli polynomials. We generalize this approach to a larger class of differential equations for which the computation of periodic solutions is also sharp, finite and effective.

Improvement in Accuracy of ISAR Image Formation Using the Shooting and Bouncing Ray

Since the introduction of a fast Fourier transform (FFT)-based convolution scheme between an impulse train and a ray spread function for the inverse synthetic aperture radar (ISAR) image formation using shooting and bouncing ray (SBR), remarkable progress has been made in reducing calculation time. However, because of an interpolation algorithm, which is essential to the FFT process, it necessarily causes the distortion of image. The present work is an attempt to generate an accurate image without loss of calculation time efficiency. Specifically, by removing dominant interpolation error contribution from the prior ray spread function, the distortion is prevented without the use of the time-consuming higher-order interpolation or high oversampling. The proposed scheme is simulated for several 3-D CAD models and demonstrated by comparing the image using the proposed and existing scheme under the same conditions.

DSP-Based Approach to Generating Computer Model of Impulse Noise Using Kernel Data Sequence

In this paper, we present a new computer model to simulate the impulse-type noise that appears in bursts on a high- voltage (HV) power line during transient and emergency situations. The computer model is designed for investigations of the effects of impulse noise on communication channels implemented over an HV power line. The simulation process relies on an authentic record of measured noise whose modified replicas we use to compose a train of short-time impulses evenly distributed in time. The recorded noise sequence is referred to as a kernel data sequence over which we apply digital-signal-processing (DSP) techniques to randomize its length and its amplitudes. Noise impulses produced by the simulator achieve and retain the sharp front ends and spectral properties of the original noise. A variable digital filter is implemented to examine the influences of impulse noise on communication channels. Performances of simulated noise have been compared with those of measured noise published in CIGRE, IEEE, and IEC documents. Comparisons demonstrate a good agreement between the characteristics of measured and simulated noise.

Threshold conditions, energy spectrum and bands generated by locally periodic Dirac comb potentials

We derive expressions for polynomials governing the threshold conditions for different types of locally periodic Dirac comb potentials comprising of attractive and combination of attractive and repulsive delta potential terms confined symmetrically inside a one dimensional box of fixed length. The roots of these polynomials specify the conditions on the potential parameters in order to generate threshold energy bound states. The mathematical and numerical methods used by us were first formulated in our earlier works and it is also very briefly summarized in this paper. We report a number of mathematical results pertaining to the threshold conditions and these are useful in controlling the number of negative energy states as desired. We further demonstrate the correlation between the distribution of roots of these polynomials and negative energy eigenvalues. Using these results as basis, we investigate the energy bands in the positive energy spectrum for the above specified Dirac comb potentials and also for the corresponding repulsive case. In the case of attractive Dirac comb the base energy of the each band excluding the first band coincides with specific eigenvalue of the confining box whereas in the repulsive case it coincides with the band top. We deduce systematic correlation between band gaps, band spreads and box eigenvalues and explain the physical reason for the vanishing of band pattern at higher energies. In the case of Dirac comb comprising of orderly arranged attractive and repulsive delta potentials, specific box eigenvalues occur in the middle of each band excluding the first band. From our study we find that by controlling the number and strength parameters of delta terms in the Dirac comb and the size of confining box it is possible to generate desired types of band formations. We believe the results from our systematic analysis are useful and relevant in the study of various one dimensional systems of physical interest in areas like nanoscience.

Ultrasonic propagation in finite-length granular chains

A narrowband ultrasound source has been used to generate solitary wave impulses in finite-length chains of spheres. Once the input signal is of sufficient amplitude, both harmonics and sub-harmonics of the input frequency can be generated as non-linear normal modes of the system, allowing a train of impulses to be established from a sinusoidal input. The characteristics of the response have been studied as a function of the physical properties of the chain, the input waveform and the level of static pre-compression. The results agree with the predictions of a theoretical model, based on a set of discrete dynamic equations for the spheres for finite-length chains. Impulses are only created for very small pre-compression forces of the order of 0.01N, where strongly non-linear behaviour is expected.

CaMKII Controls Whether Touch Is Painful.

The sensation of touch is served by specialized sensory neurons termed low-threshold mechanoreceptors (LTMRs). We examined the role of CaMKII in regulating the function of these neurons. Loss of CaMKII function, such as occurred in rats during sensory deprivation, elevated the generation and propagation of impulses by LTMRs, and altered the spinal cord circuitry in such a way that low-threshold mechanical stimuli produced pain behavior. Because limbs are protected from use during a painful condition, this sensitization of LTMRs may perpetuate pain and prevent functional rehabilitation.

All Aboard the Impulse Train: A Retrospective Analysis of the Two-Channel Title Music Routine in Manic Miner

The launch of the ZX Spectrum in the UK in April 1982 almost single-handedly kick-started the British computer games industry. Launched to compete with technologically superior rivals from Acorn and Commodore, the Spectrum had price and popularity on its side, and became a runaway success. However, one feature of the Spectrum that was found lacking was its sound hardware—just a single channel of 1-bit sound playback. Few improvements to the machine’s hardware were made during the first generation of Spectrum titles. Programmers soon realised, however, that with clever machine coding, the Spectrum’s speaker could do more than that for which it was originally designed. This creativity, born from constraint, represents a very real example of technology (or rather, limited technology) as a driver for creativity. These solutions gave rise to a characteristic sound that in time defined the aesthetic of ZX Spectrum music. At the time, there was little interest in the formal study of either the technologies that support computer games, or of the social and cultural phenomena that surround them. This knowledge gap is redressed in this retrospective study through a deconstruction and analysis of a key turning point in the musical life of the ZX Spectrum. The title music for Manic Miner was the first attempt at a true two-channel sound routine on the platform, and so marked the point at which music moved from being largely functional and utilitarian, to becoming an important and expressive dimension of the Spectrum gaming experience. This paper begins with an overview of 1-bit sound and the range of tones that are natively supported by a 1-bit system, followed by a demonstration of how these can be extended using frequency dividers and counters to create time-varying tones and pseudo two-channel sound. The limitations of this technique are highlighted, and the key adaptations that would make it a viable approach for two-channel sound in later games are outlined.

Postsynaptic Potentiation in Mouse Motor Synapses Induced by ATP Accumulation in Synaptic Cleft.

In mouse motor synapses, a non-selective purinoceptor antagonist suramin increased the quantum content of endplate potentials (EPP) without changing the time course of synaptic potentials. An ectonucleotidase inhibitor ARL 67156 had no effect on the amplitude and quantum content of EPP and miniature endplate potentials (mEPP) evoked by single stimuli, but significantly prolonged their duration. Long-term high-frequency stimulation of the nerve in the presence of ARL 67156 persistently increased the amplitude and duration of EPP during the train of impulses, but did not change their quantum content. ATP-γ-S, a non-hydrolyzed ATP analogue, significantly increased the amplitudes and prolonged the rising and falling phases of EPP and mEPP. The ATP-induced postsynaptic potentiation in neuromuscular transmission can result from the increase in ATP content and its longer presence in the synaptic cleft.

Modulational instability in dispersion-kicked optical fibers

We study, both theoretically and experimentally, modulational instability in optical fibers that have a longitudinal evolution of their dispersion in the form of a Dirac delta comb. By means of Floquet theory, we obtain an exact expression for the position of the gain bands, and we provide simple analytical estimates of the gain and of the bandwidths of those sidebands. An experimental validation of those results has been carried out in several microstructured fibers specifically manufactured for that purpose. The dispersion landscape of those fibers is a comb of Gaussian pulses having widths much shorter than the period, which therefore approximate the ideal Dirac comb. Experimental spontaneous modulational instability spectra recorded under quasicontinuous wave excitation are in good agreement with the theory and with numerical simulations based on the generalized nonlinear Schr\"odinger equation.

Serotonin release from the neuronal cell body and its long-lasting effects on the nervous system

Serotonin, a modulator of multiple functions in the nervous system, is released predominantly extrasynaptically from neuronal cell bodies, axons and dendrites. This paper describes how serotonin is released from cell bodies of Retzius neurons in the central nervous system (CNS) of the leech, and how it affects neighbouring glia and neurons. The large Retzius neurons contain serotonin packed in electrodense vesicles. Electrical stimulation with 10 impulses at 1 Hz fails to evoke exocytosis from the cell body, but the same number of impulses at 20 Hz promotes exocytosis via a multistep process. Calcium entry into the neuron triggers calcium-induced calcium release, which activates the transport of vesicle clusters to the plasma membrane. Exocytosis occurs there for several minutes. Serotonin that has been released activates autoreceptors that induce an inositol trisphosphate-dependent calcium increase, which produces further exocytosis. This positive feedback loop subsides when the last vesicles in the cluster fuse and calcium returns to basal levels. Serotonin released from the cell body is taken up by glia and released elsewhere in the CNS. Synchronous bursts of neuronal electrical activity appear minutes later and continue for hours. In this way, a brief train of impulses is translated into a long-term modulation in the nervous system.

Effect of acetylcholine receptors on the pain-related electrical activities in the hippocampal CA3 region of morphine-addicted rats.

To determine the effect of acetylcholine (ACh), pilocarpine, and atropine on pain evoked responses of pain excited neurons (PEN) and pain inhibited neurons (PIN) in hippocampal CA3 region of morphine addicted rats. Female Wistar rats, weighing between 230-260 g were used in this study. Morphine addicted rats were generated by subcutaneous injection of increasing concentrations of morphine hydrochloride for six days. Trains of electrical impulses applied to the sciatic nerve were used as noxious stimulation and the evoked electrical activities of PEN or PIN in hippocampal CA3 area were recorded using extracellular electrophysiological recording techniques in hippocampal slices. The effect of acetylcholine receptor stimulation by ACh, the muscarinic agonist pilocarpine, and the muscarinic antagonist atropine on the pain evoked responses of pain related electrical activities was analyzed in hippocampal CA3 area of morphine addicted rats. Intra-CA3 microinjection of ACh (2 μg/1 μl) or pilocarpine (2 μg/1 μl) decreased the discharge frequency and prolonged the firing latency of PEN, but increased the discharge frequency and shortened the firing inhibitory duration (ID) of PIN. The intra-CA3 administration of atropine (0.5 μg/1 μl) produced opposite effect. The peak activity of cholinergic modulators was 2 to 4 min later in morphine addicted rats compared to peak activity previously observed in normal rats. ACh dependent modulation of noxious stimulation exists in hippocampal CA3 area of morphine addicted rats. Morphine treatment may shift the sensitivity of pain related neurons towards a delayed response to muscarinergic neurotransmission in hippocampal CA3 region.

Eulerian-based virtual visual sensors to detect natural frequencies of structures

Natural frequency of vibration data are often used to study the behavior of structures. They are also used to calibrate finite element models and some studies have proposed that the presence and location of damage can be estimated using these data. Along this line, we earlier proposed the concept of Eulerian-based virtual visual sensors to estimate natural frequencies of structural vibrations based on the change of pixel intensity captured in a digital video. Benefits of this approach are that it allows for distributed sensing and is contactless. However, as intensity does not reflect any physical quantity, such as displacement, and the range of values is difficult to control, the signal-to-noise ratio (SNR) can be relatively low. Furthermore, impulsive changes of intensity caused by large deformations compared to the pixel size can result in an impulse train in the frequency domain which leads to ambiguity in determining peak frequencies. As a result, it is often only possible to estimate the first fundamental mode of vibration. In this paper, we present strategies using targets mounted to the structure combined with signal processing methods that significantly improve the SNR and allow for detecting higher natural frequencies of vibration. The concepts, their mathematical background, laboratory tests to prove the accuracy and enhancement of SNR, as well as an example of an in-service pedestrian bridge are presented and discussed.

A biorthogonal wavelet design technique using Karhunen–Loéve transform approximation

The lifting style biorthogonal wavelet implementation has a nice property of enabling flexible design; it is immediately reversible and has a simple relation to subband filters. In this work, we present a method to design prediction (P) and update (U) filters of two-channel lifting structures by minimising the difference between Block Wavelet Transform (BWT) matrix of the wavelet and the Karhunen–Loéve Transform (KLT) of a stochastic process with certain autocorrelation. Here, BWTs are transform matrices that are generated by constructing columns through balanced wavelet trees fed by shifted impulse trains. Although wavelets already have fast implementations through subband filtering or lifting, parametric optimisation of the filter coefficients is still possible through indirectly mimicking the corresponding wavelet and a class of signals with certain KLT. This paper describes the above optimisation by putting constraints on the P and U filters for regularity and constructing the filter coefficients in a least-squares sense. In this part of the paper, the iterated orthogonality constraint over the BWT is resolved with a generalised 12k+1-tap/6k+1-tap P / U construction with numerical results for the 4×4 and 8×8 BWT cases. Experimental approximation to several KLT cases with numerical results in terms of filter coefficients, their spectral behaviour, compaction gain, etc. are provided.

The infogram: Entropic evidence of the signature of repetitive transients

A classical symptom of rotating machines faults in vibration signals is the presence of repetitive transients, whose distinctive signature is both impulsive and cyclostationary. Typical approaches for their detection proceed in the time or frequency domains, with tools such as the spectral kurtosis, the kurtogram, or the envelope spectrum. The object of this paper is to extend and somehow connect these concepts in order to capture the signature of repetitive transients in both domains. Motivated by ideas borrowed from the field of thermodynamics where transients are seen as departures from a state of equilibrium, it is proposed to measure the negentropy of the squared envelope (SE) and of the squared envelope spectrum (SES) of the signal. This defines the SE infogram, the SES infogram, and their average which is theoretically maximum for a Dirac comb according to Hirschman’s uncertainty principle. It is demonstrated that the joint consideration of the infograms significantly extends the domain of applicability of the kurtogram, in particular to situations corrupted with impulsive noise or when the relaxation time of the transients is low as compared to their rate of repetition. This is illustrated on both synthetic and actual vibration signals. This paper is part of a special issue in honor of Professor Simon Braun and pays tribute to his early contribution to the field of mechanical signature analysis.

Pulse-to-pulse alignment based on interference fringes and the second-order temporal coherence function of optical frequency combs for distance measurement.

A pulse-to-pulse alignment method based on interference fringes and the second-order temporal coherence function of optical frequency combs is proposed for absolute distance measurement. The second-order temporal coherence function of the pulse train emitted from optical frequency combs is studied. A numerical model of the function is developed with an assumption of Gaussian pulse and has good agreement with experimental measurements taken by an ordinary Michelson interferometer. The experimental results show an improvement of standard deviation of peak finding results from 27.3 nm to 8.5 nm by the method in ordinary laboratory conditions. The absolute distance measurement with the pulse-to-pulse alignment method is also proposed and experimentally proved.

Acoustic Assessment of Beauveria bassiana (Hypocreales: Clavicipitaceae) Effects on Rhynchophorus ferrugineus (Coleoptera: Dryophthoridae) Larval Activity and Mortality.

Rhynchophorus ferrugineus (Olivier) (Coleoptera: Dryophthoridae) is an economically important pest of palm trees in the subtropics. Beauveria bassiana (Balsamo-Crivelli) Vuillemin (Hypocreales: Clavicipitaceae), has been shown to be pathogenic against R. ferrugineus in laboratory and field studies. However, because they remain inside the trunks until adulthood, the slowing of feeding and increases in mortality of internally feeding R. ferrugineus larvae over time after B. bassiana treatment has not been established. To explore the potential of acoustic methods to assess treatment effects, sound impulses produced by untreated, 10(4)-, and 10(6)-conidia ml(-1) B. bassiana-treated larvae in palms were recorded for 23 d, after which the palms were dissected and the larvae examined. Analyses were performed to identify trains of impulses with characteristic patterns (bursts) produced frequently by moving and feeding larvae but only rarely (3-8% of the larval rate) by interfering background noise or tree vibrations. The rates of bursts, the counts of larval impulses per burst, and the rates of impulses in bursts decreased significantly over time in both B. bassiana treatments but not in the control. This supports a hypothesis that larvae had briefer movement and feeding bouts as they became weaker after infection, which reduced the counts of larval impulses per burst, the rates of bursts, and the rates of impulses in bursts. There is considerable potential for use of acoustic methods as tools for nondestructive assessment of effects of biological control treatments against internally feeding insect pests.

Rhythmic analysis for click train detection and source separation with examples on beluga whales

Passive acoustic monitoring systems are used to study cetaceans through the sounds they produce. Among them, toothed whales emit sequences of acoustic impulses having a rhythmic pattern. As they generally live in pods, click trains from several individuals are often interleaved and recorded together with additional natural or anthropogenic impulsive sources. This paper presents an algorithm that uses the rhythmic properties of odontocete click trains for detecting rhythmic impulse trains embedded in other impulse sounds and de-interleaving click trains from simultaneous clicking odontocetes. The contributions of the article are: (1) a method to detect the presence/absence of rhythmic click trains and to characterize the time – Inter Click Interval (ICI) pattern of click trains; (2) an analytical analysis of the performances of this method (jitter, length of click trains); (3) the demonstration of its efficiency on real data with wild beluga whales recorded in Canada.

The use of automated system for EEG analysis and feedback cerebral stimulation to stop epileptiform activity in WAG/Rij rats.

Original software program is described, which revealed EEG activity characteristic of the onset of epileptic seizure and turned on electrical stimulation of the nucleus basalis of Meynert in WAG/Rij rats with congenital absence epilepsy. The program reliably detected the onset of seizure and automatically stopped it with a high-frequency train of electrical impulses (100-150 Hz). Thus, a feedback system of deep brain stimulation has been developed to stop early manifestations of absence epileptiform seizures. The study can be a base to develop an implanted apparatus to automatically analyze EEG and stimulate the brain to stop the epileptic seizures.