Presence Of Jitter Research Articles

Uncertainty of the initial phase estimation of a sinewave in the presence of phase noise, additive noise or jitter

This paper presents the derivation of a simple analytical expression for the precision of the initial phase estimates obtained through a least-squares procedure. That expression depends on number of samples, phase noise standard deviation and additive noise standard deviation. This study is applicable to the estimates obtained through the sine fitting algorithm with known frequency and to the Discrete Fourier Transform algorithm. The analytical expression supplied was verified using a Monte Carlo simulation with numerically created data. The non-ideal phenomena treated in this work is the presence of jitter in the sampling instant, phase noise in the oscillator and additive noise in the system both of which must be normally distributed with a known value of standard deviation. It is useful information for an engineer in order to choose the proper number of samples to acquire to achieve a desired level of precision on the estimates made and thus carry out an efficient data acquisition with no unnecessary samples thus optimizing the test duration.

JAMS-SG

Time-triggered automotive networks use time-triggered protocols (FlexRay, TTEthernet, etc.) for periodic message transmissions that often originate from safety and time-critical applications. One of the major challenges with time-triggered transmissions is jitter, which is the unpredictable delay-induced deviation from the actual periodicity of a message. Failure to account for jitter can be catastrophic in time-sensitive systems, such as automotive platforms. In this article, we propose a novel scheduling framework (JAMS-SG) that satisfies timing constraints during message delivery for both jitter-affected time-triggered messages and high-priority event-triggered messages in automotive networks. At design time, JAMS-SG performs jitter-aware frame packing (packing of multiple signals from Electronic Control Units (ECUs) into messages) and schedules synthesis with a hybrid heuristic. At runtime, a Multi-Level Feedback Queue (MLFQ) handles jitter-affected time-triggered messages and high-priority event-triggered messages that are scheduled using a runtime scheduler. Our simulation results, based on messages and network traffic data from a real vehicle, indicate that JAMS-SG is highly scalable and outperforms the best-known prior work in the area in the presence of jitter.

Unlabeled Sensing With Random Linear Measurements

We study the problem of solving a linear sensing system when the observations are unlabeled. Specifically we seek a solution to a linear system of equations ${\mathbf{y}}= {\mathbf{A}} {\mathbf{x}} $ when the order of the observations in the vector ${\mathbf{y}}$ is unknown. Focusing on the setting in which ${\mathbf{A}}$ is a random matrix with i.i.d. entries, we show that if the sensing matrix ${\mathbf{A}}$ admits an oversampling ratio of 2 or higher, then, with probability 1, it is possible to recover ${\mathbf{x}}$ exactly without the knowledge of the order of the observations in ${\mathbf{y}}$ . Furthermore, if ${\mathbf{x}}$ is of dimension $K$ , then any $2K$ entries of ${\mathbf{y}}$ are sufficient to recover ${\mathbf{x}}$ . This result implies the existence of deterministic unlabeled sensing matrices with an oversampling factor of 2 that admit perfect reconstruction. The result is universal in that conditioned on the realization of matrix ${\mathbf{A}}$ , recovery is guaranteed for all possible choices of ${\mathbf{x}}$ . While the proof is constructive, it uses a combinatorial algorithm which is not practical, leaving the question of complexity open. We also analyze a noisy version of the problem and show that local stability is guaranteed by the solution. In particular, for every ${\mathbf{x}}$ , the recovery error tends to zero as the signal-to-noise ratio tends to infinity. The question of universal stability is unclear. In addition, we obtain a converse of the result in the noiseless case: If the number of observations in ${\mathbf{y}}$ is less than $2K$ , then with probability 1, universal recovery fails, i.e., with probability 1, there exist distinct choices of ${\mathbf{x}}$ which lead to the same unordered list of observations in ${\mathbf{y}}$ . We also present extensions of the result of the noiseless case to special cases with non-i.i.d. entries in ${\mathbf{A}}$ , and to a different setting in which the labels of a portion of the observations ${\mathbf{y}}$ are known. In terms of applications, the unlabeled sensing problem is related to data association problems encountered in different domains including robotics where it is appears in a method called “simultaneous localization and mapping”, multi-target tracking applications, and in sampling signals in the presence of jitter.

Study on directional eye movements in non‐frontal face images for eye‐controlled interaction

AbstractDirectional eye movements based eye‐controlled interaction focuses on interpreting the horizontal, vertical, and diagonal eye movements or their combinations as inputs to design user interfaces for people who suffer with severe mobility disabilities. In this paper, we take into consideration the inherent eye jitter and evaluate the accuracy of dynamic tracking of horizontal, vertical, diagonal, and rectangular eye movements prior to using them. We observe that the rectangular eye gesture composed of short horizontal and vertical eye movements has the best tracking accuracy in the presence of jitter. Finally, we present methods for identifying horizontal and vertical eye movements based on the trajectory of eye pupil centers from non‐frontal face images. We find that the methods are robust and effective within ±20°deflective azimuths of non‐frontal faces. This effectiveness is demonstrated by using the rectangular eye gesture as an interface to perform a painting task.

Performance Analysis and Enhancement of TCP in Presence of Jitter in Wireless Networks

Performance Analysis and Enhancement of TCP in Presence of Jitter in Wireless Networks

A periodic jump-based rendezvous algorithm in cognitive radio networks

An important issue in designing multichannel MAC protocols for Opportunistic Spectrum Access (OSA) is the synchronization between Secondary Users (SUs). Synchronization can be performed in two phases: the initial handshaking, and then the synchronous hopping across available channels. In this paper, we address the problem of initial handshaking through the approach called “blind rendezvous”. We first introduce a role-based solution by constructing two channel hopping sequences. The secondary transmitter and receiver jump across channels according to these two sequences. The proposed algorithm guarantees rendezvous in at most (C+1)2 time slots (where C is the number of channels) and two SUs have a chance to rendezvous in each successive period of C time slots. We show that this property of constructed sequences leads to a lower average time-to-rendezvous (TTR) for the proposed algorithm in comparison to other related works. We also devise a solution to ensure rendezvous in the presence of jitter. Next, we extend the proposed algorithm to the non-role-based scenario. Simulation results show that it has the best performance with respect to existing works in various traffic patterns of primary users. Besides, it is the most predictable solution due to its low variance of TTR.

Background subtraction by combining Temporal and Spatio-Temporal histograms in the presence of camera movement

Background subtraction is the classical approach to differentiate moving objects in a scene from the static background when the camera is fixed. If the fixed camera assumption does not hold, a frame registration step is followed by the background subtraction. However, this registration step cannot perfectly compensate camera motion, thus errors like translations of pixels from their true registered position occur. In this paper, we overcome these errors with a simple, but effective background subtraction algorithm that combines Temporal and Spatio-Temporal approaches. The former models the temporal intensity distribution of each individual pixel. The latter classifies foreground and background pixels, taking into account the intensity distribution of each pixels' neighborhood. The experimental results show that our algorithm outperforms the state-of-the-art systems in the presence of jitter, in spite of its simplicity.

Resolution of ITD detection: stochastic vs. exquisite system

Differences in arrival times of a sound at the two ears (Interaural Time Differences, ITDs) are utilized by mammals to determine the location of low-frequency sound source in the horizontal dimension [4]. Simple calculation shows that to achieve psychophysically revealed accuracy of sound localization, binaural auditory system have to detect ITDs in the order of just a few tens of microseconds. It has long been assumed that such remarkable temporal resolution is the result of ITD encoding by systematically organized arrays of fast neurons - “coincidence detectors” that receive inputs from the two ears via axons of variable length - “delay lines” and create a neural “map” of physiological ITDs. However, despite its wide acceptance, an increasing number of recent morphological and physiological studies in mammals report findings that can not be interpreted in the framework of this classical coincidence detector concept (reviewed in [2]). Therefore, neural mechanisms of the mammalian auditory system underlying high-resolution ITD detection are still not fully understood. Here, we continue to consider an alternative ITD detection mechanism based on a population coding strategy [5], according to which ITDs are encoded by the relative “activity” levels within bilaterally located populations of binaural sluggish (slow) neurons. To implement studied ITD detection mechanism we employ biologically inspired computational model that simulates the behavior of two symmetric neural populations of the auditory system. Every single neuron model of each population has membrane time constant of >1 ms and receives the balanced excitatory-inhibitory (EI) synaptic inputs carrying ITD. The parameters of neuron [3] and synapse [1] models are turned to mimic pure trough-type activity of EI neurons, i.e., no (or minimal) responses occur when “ipsilateral” excitation and “contralateral” inhibition are near coincidence. Our previous theoretical and modeling studies have shown that precise distribution (oppositely directed linear gradients) of the conductance value of excitatory and inhibitory synapses within each population allows the proposed model to detect ITD with submillisecond precision. It was also revealed that presence of jitter (related to the dynamic travel time deviation of ipsi- and contralateral signals) or neuronal noise from the physiological range does not have dramatic influence on ITD detection accuracy. In this work, we focus on the further analysis of stochastic and noise processes in the auditory system and present a computational evidence indicating the necessity to reassess the role of stochasticity in ITD processing. We demonstrate that microsecond order resolution of ITD detection, based on the population coding mechanism, can be accomplished by the auditory system without exquisite tunings of synapses or/and axon lengths. It is also shown that biologically relevant levels of both intrinsic neuronal noise and random time jitter in the synaptic input underlie ITD detection acuity similar to that observed in the model with a precise as well as a random balance of excitatory and inhibitory synaptic inputs. Thus, the results suggest that the considered stochastic processes can play crucial role as complementary/replaceable sources of “perturbation” for the sluggish neuron based populations; that is needed for high-resolution ITD detection.

Binary Phase Detector Gain in Bang-Bang Phase-Locked Loops With DCO Jitter

Bang-bang phase-locked loops are hard nonlinear systems due to the nonlinearity introduced by the binary phase detector (BPD). In the presence of jitter, the nonlinear loop is typically analyzed by linearizing the BPD and applying linear transfer functions in the analysis. In contrast to a linear phase detector, the linearized gain of a BPD depends on the rms jitter and the type of jitter (either nonaccumulative or accumulative). Previous works considered the case of nonaccumulative reference clock jitter and showed that the BPD gain is inversely proportional to the rms jitter when the latter is small or large. In this brief, we consider the case of accumulative digitally-controlled oscillator (DCO) jitter and derive an asymptotic closed-form expression for the BPD gain, which becomes exact in the limit of small and large jitter. Contrary to the reference clock jitter case, the BPD gain is constant for small DCO jitter and is inversely proportional to the square of jitter for large DCO jitter; in the latter case, the timing jitter has a normal Laplace distribution.

Analysis of Clock Jitter in Continuous-Time Sigma–Delta Modulators

One of the factors limiting the performance of continuous-time sigma-delta modulators (CTSDMs) is clock jitter. This jitter can be classified as synchronous and accumulated/long-term jitter. A clock that is derived from a phase-lock loop contains both types of jitter. In this paper, we present a framework that can be used to obtain the output spectrum in the presence of jitter, either synchronous or accumulated or a combination of both. First, a general expression for the output power spectral density (PSD) of the CTSDM in the presence of clock jitter is derived. Based on this, analytical expressions for the output PSD are obtained for particular cases of synchronous and long-term jitter. These are validated against behavioral simulations.

Linear phase matched filter design with causal real symmetric impulse response

Linear phase matched filter design for pulse transmission without Intersymbol Interference is presented. The delayed time-domain raised-cosine pulse is considered for the output of the shaping filter at the transmitter. To approximate the transmit filter, a linear phase denominator polynomial is used, and transmission zero pairs are placed on the j ω -axis in accordance with the attenuation response of the time-domain raised-cosine pulse. The combination of even symmetry of the time response, and j ω -axis transmission zero pairs leads to a linear phase pulse shaping filter which is its own match. The maximum number of finite transmission zero pairs for zero pulse amplitude at t = 0 is derived. The generated pulse is time-limited and has negligible energy outside the main lobe, and better performance in the presence of jitter than the standard raised-cosine spectrum pulse. The received pulse is time-limited and band-limited.

Spectral Analysis of Randomly Sampled Signals: Suppression of Aliasing and Sampler Jitter

Nonuniform sampling can facilitate digital alias-free signal processing (DASP), i.e., digital signal processing that is not affected by aliasing. This paper presents two DASP approaches for spectrum estimation of continuous-time signals. The proposed algorithms, named the weighted sample (WS) and weighted probability (WP) density functions, respectively, utilize random sampling to suppress aliasing. Both methods produce unbiased estimators of the signal spectrum. To achieve this effect, the computational procedure for each method has been suitably matched with the probability density function characterising the pseudorandom generators of the sampling instants. Both proposed methods are analyzed, and the qualities of the estimators they produce have been compared with each other. Although none of the proposed spectrum estimators is universally better than the other one, it has been shown that in practical cases, the WP estimator produces generally smaller errors than those obtained from WS estimation. A practical limitation of the approaches caused by the sampling-instant jitter is also studied. It has been proven that in the presence of jitter, the theoretically infinite bandwidths of WS and WP signal analyses are limited. The maximum frequency up to which these analyses can be performed is inversely proportional to the size of the jitter.

Recovering signals from inner products involving prolate spheroidals in the presence of jitter

The paper deals with recovering band- and energy-limited signals from a finite set of perturbed inner products involving the prolate spheroidal wavefunctions. The measurement noise (bounded by δ) and jitter meant as perturbation of the ends of the integration interval (bounded by γ) are considered. The upper and lower bounds on the radius of information are established. We show how the error of the best algorithms depends on γ and δ. We prove that jitter causes error of order Ω 3 / 2 γ, where [-Ω,Ω] is a bandwidth, which is similar to the error caused by jitter in the case of recovering signals from samples.

Rotation Vector in Attitude Estimation

An alternative derivation of the spacecraft attitude determination filter is developed to avoid questions of quater-nion normalization or attitude matrix orthogonality constraints, quaternion covariance, and subterfuges used to circumvent these problems. This derivation is based on the Bortz equation for the rotation vector. Because the rotation vector is an unconstrained representation of attitude, the aforementioned questions do not arise. Singularities in the state dynamics equation are avoided by maintaining the predicted body attitude as the inertial reference for the filter. A simple discrete solution to the Bortz equation provides accurate attitude propagation for highly maneuverable spacecraft and also in the presence of jitter.

Optimum divergence angle of a Gaussian beam wave in the presence of random jitter in free-space laser communication systems.

The average bit error rate (BER) of optical communication systems is considered in the presence of random angular jitter. First, the received power and the BER in the absence of jitter are reviewed. Then the average BER is obtained in the presence of circularly symmetric, normally distributed jitter by using the probability density function of the optical signal. By minimizing the power penalty for average BER, the optimum ratio of the divergence angle of the laser beam to the random angular jitter at the desired BER is obtained. An analytic approximation of the optimum ratio is derived as a function of the desired average BER. The results can be used for designing the link budget of optical communication and tracking channels in the presence of jitter.

Psychoacoustical evaluation of PSOLA. II. Double-formant stimuli and the role of vocal perturbation.

This article presents the results of listening experiments and psychoacoustical modeling aimed at evaluating the pitch synchronous overlap-and-add (PSOLA) technique. This technique can be used for simultaneous modification of pitch and duration of natural speech, using simple and efficient time-domain operations on the speech waveform. The first set of experiments tested the ability of subjects to discriminate double-formant stimuli, modified in fundamental frequency using PSOLA, from unmodified stimuli. Of the potential auditory discrimination cues induced by PSOLA, cues from the first formant were found to generally dominate discrimination performance. In the second set of experiments the influence of vocal perturbation, i.e., jitter and shimmer, on discriminability of PSOLA-modified single-formant stimuli was determined. The data show that discriminability deteriorates at most modestly in the presence of jitter and shimmer. With the exception of a few conditions, the trends in these data could be replicated by either using a modulation-discrimination or an intensity-discrimination model, dependent on the formant frequency. As a baseline experiment detection thresholds for jitter and shimmer were measured. Thresholds for jitter could be replicated by using either the modulation-discrimination or the intensity-discrimination model, dependent on the (mean) fundamental frequency of stimuli. The thresholds for shimmer could be accurately predicted for stimuli with a 250-Hz fundamental, but less accurately in the case of a 100-Hz fundamental.

Approximating Band- and Energy-Limited Signals in the Presence of Jitter

This paper deals with recovering band- and energy-limited signals from a finite set of their perturbed samples taken at slightly wrong points. The perturbations in sample points reading (called jitter) and in the measurements of the corresponding samples are assumed to be bounded byγandδ, respectively. The goal is to analyze how the minimal worst-case recovery error depends onγandδ. This is accomplished by proving tight upper and lower bounds on the diameter of information. The main conclusion is that the jitter causes the error of orderγΔ3/2+δ, whereΔis the bandwidth.

Minimizing the effects of jitter in distributed hard real-time systems

In this paper we present a study of the effects caused on distributed real-time systems by the presence of jitter in the activation of tasks and messages. We show that although jitter has usually a small impact on the schedulability of single-processor systems, in distributed architectures the worst-case response times are significantly delayed. Reducing or eliminating jitter in these systems can increase the schedulability of the system up to 50% more than when jitter is permitted. The delay effects caused by jitter can be prevented by using a bandwidth-preserving scheduling algorithm such as the sporadic server. Since this kind of scheduling policy is not designed for communication networks, we describe in this paper how to adapt and implement the sporadic server algorithm on communication networks. Using the sporadic server both in the processors and networks, we can build distributed systems with up to 100% utilization of the CPUs and communication resources, while still guaranteeing that hard real-time requirements are met.

Optimum FIR filter for sampled signals in presence of jitter

Abstract The requirements of the integrated readout electronics for calorimetry at high luminosity hadron colliders pose new challenges both to hardware design and to the performance of signal processing algorithms. Both aspects have been treated in detail by the FERMI(RD16) 1 collaboration [C. Alippi et al., Nucl. Instr. and Meth. A 344 (1994) 180], from which this work has been motivated. The estimation of the amplitude of sampled signals is usually performed with a digital FIR filter, or with a more sophisticated non linear digital filter using FIR filters as building blocks [S.J. Inkinen and J. Niittylahti, Trainable FIR-order statistic hybrid filters, to be published in IEEE Trans. Circuits and Systems; H. Alexanian et al., FERMI Collaboration, Optimized digital feature extraction in the FERMI microsystem Nucl. Instr. and Meth. A 357 (1995)]. In presence of significant signal phase jitter with respect to the clock, the phase dependence of the filter output can be a major source of error. This is especially true for measurements of large amplitudes for which the effect of electronic noise becomes negligible. This paper reports on the determination of digital FIR filters that optimize the signal over noise ratio due to known jitter distributions for different filter lengths. As the presence of electronic noise is neglected, the results are mainly relevant for measurements of large signals.

Optimum truncation of a Gaussian beam in the presence of random jitter

I consider the far-field (or focal plane) irradiance distribution of a Gaussian beam that is truncated by a circular aperture in the presence of random angular jitter. First, for absence of jitter, I derive an accurate analytic approximation for the irradiance distribution within the main lobe of the beam for the case in which the beam diameter is less than the aperture diameter. Then I obtain the corresponding mean irradiance distribution in the presence of circularly symmetric normally distributed jitter. By maximizing the on-axis intensity I obtain the optimum ratio of the beam diameter to the aperture diameter in the presence of jitter and present results for the corresponding maximum on-axis intensity and encircled power as a function of the jitter statistics.