Random Jitter Research Articles

Jitter Characteristics of Mark Edge Recording on MO Disks

Edge shift and jitter characteristics have been examined using both conventional disks and an overwritable disk with three exchange-coupled layers. Edge jitter consists of random jitter, edge shifts dependent on data patterns (thermal interference), and edge shifts independent of data patterns (fluctuations of temperature or light spot control). Write compensation is an effective means of correcting shifts depending on data patterns. The shifts which are independent of data patterns can be rendered negligible in comparison with random jitter by using an edge detection method in which the leading and trailing edges are detected independently. The results were the same for the overwritable disk. The possibility of applying edge recording in magnetooptic disk systems was thus confirmed.

Sampling jitter in Fourier-transform spectrometers: spectral broadening and noise effects

The effect of sampling jitter induced by frequency fluctuations of the reference laser is analyzed theoretically. It is shown that the spectral broadening of the lines is small enough to permit the use of single-mode laser diodes in medium-to-high-resolution spaceborne instruments. The same mathematical formalism is used to give a new insight into the analysis of the spectral noise induced by random sampling jitter caused by detector and electronic noise.

Simple method to start and maintain self-mode-locking of a Ti:sapphire laser

By periodically moving one of the end mirrors of a Ti:sapphire laser using a shaker, we have been able to start and maintain self-mode-locking of the laser. The resulting laser is stable over a long period with low-amplitude noise (3.3%) and low random timing jitter (4.8 ps). In addition, there is a deterministic timing variation on the order of subnanoseconds, caused by the moving mirror, which can be reduced by employing a feedback system. Pulses as short as 43 fs have been obtained.

Determining the coherence of micropulses

A technique based on analysis of the cross spectra of single-use data from pulsars is described which can be used to measure the coherence properties of, and search for coherent periodicities in, pulsar signals. Several simulated pulsar models are constructed and analyzed to test the technique. From an analysis of 2000 consecutive pulses from PSR 2016 + 28 it is concluded that the micropulse coherence time of 430 MHz is less than the spin period for this object. This could could be consistent with a coherent model if the random phase jitter in such a model is 35 percent or more of the micropulse quasi-periodicity. The subpulse separation of roughly 10 ms is coherent across 4-5 pulse periods and is reasonably consistent with a model of subpulse drift that allows for variation about some mean drift rate. A two-component shot-noise model can reproduce much of the structure seen in the individual pulses as well as the spectra of PSR 2016 + 28.

Simulations to demonstrate reduction of the Gordon–Haus effect

The superposition of spontaneous emission noise on a train of soliton pulses produces a random change of the center frequency of the soliton spectrum that causes a change of the group velocity of individual solitons, which in long-light-wave systems translates into a random jitter of the position of the pulses at the receiver. This phenomenon is known as the Gordon-Haus effect. If uncontrolled, the Gordon-Haus effect sets a definite limit on the permissible data rate or on the length of soliton-based light-wave systems. Recently Kodama and Hasegawa [Opt. Lett. 17, 31 (1992)] have shown that the Gordon-Haus effect can be suppressed by placing filters along the fiber that reduce the frequency jitter and the concomitant group-velocity changes. We demonstrate the reduction of the Gordon-Haus effect by computer simulations.

On the determination of the worst sampling error in a communication system for pulse amplitude modulated signals. Part II: The finite dimensional model

This paper is dedicated to the problem of optimizing the transmission properties of a Pulse Amplitude Modulation (PAM) system. The system is disturbed by a random timing jitter in the sampling device which periodically evaluates the continuous output signal at discrete times. Mathematically the timing jitter is a random variable with unknown probability distribution. So, our optimization problem turns out to be actually a minimax problem, for which mathematical game theory with its powerful concepts becomes the suitable frame for our analysis.

Why do isoluminant stimuli appear slower?

There is ample evidence that the perception of movement, both real and apparent, is substantially impaired at isoluminance. Models of movement perception require spatial and temporal information about the stimulus. We ask whether changes at isoluminance result from a spatial or a temporal error or uncertainty. Reaction times to three kinds of stimulus were measured: (a) temporal stimuli, such as the onset of a square in a known location; (b) spatial stimuli, a vernier displacement of two squares; and (c) spatiotemporal stimuli, moving squares either starting or stopping. The results suggest that there is relatively little effect of isoluminance on purely temporal tasks (a). Longer reaction times were, however, obtained for detecting vernier offset (b). The reaction times to moving stimuli (c) were also slower at isoluminance to an extent that implies that perceived velocity at isoluminance is approximately 30% less than that seen at 8% contrast. The slowing of reaction times at isoluminance could be mimicked by adding random positional jitter to a nonisoluminant moving stimulus and also by presenting a low-contrast monochromatic stimulus. A simple explanation of the data is given in terms of a motion-detecting unit coupled to a temporal integrator. It is shown how such a unit can encode perceived velocity. The results of these experiments suggest that the neural coding of isoluminant stimuli is similar to that of low-contrast luminance stimuli and therefore that isoluminance may not be an effective method to find out whether specific visual mechanisms are color-blind.

A time-frequency formulation of optimum detection

A time-frequency formulation is proposed for the optimum detection of Gaussian signals in white Gaussian noise. By choosing the Wigner-Ville distribution as the basic time-frequency tool, it is shown that the corresponding receivers generally take the form of a correlation between time-frequency structures, matching mathematical optimality with a physically meaningful interpretation. The case of low SNR is examined and various examples are considered: deterministic signal, Rayleigh fading signal, random jitter, and random time-varying channel. A general class of time-frequency receivers is proposed which admits as limiting cases different known structures, and its suboptimum performance is evaluated. Possible extensions to more elaborate situations (including parameter estimation) are mentioned. >

Optical beam wave propagation through complex optical systems

20We describe a novel formulation of light beam propagation through any complex optical system that can be described by an ABCD ray-transfer matrix. Within the paraxial approximation, optical propagation can be formulated in terms of a Huygens principle expressed in terms of the ray-transfer ABCD matrix elements of the optical system. We extend and generalize previous treatments to include the effects of finite-sized limiting apertures (i.e., diffractive screens) in the optical train, tilt and random jitter of the optical elements, and distributed random inhomogeneities along the optical path (e.g., clear air turbulence and aerosols). In the presence of limiting apertures the ABCD matrix elements of the optical system are complex. For the case of laser beam propagation and Gaussian-shaped limiting apertures in the optical train, we obtain analytical expressions for both the spot radius and the wave-front radius of curvature at an arbitrary observation plane and give illustrative examples of practical concern. In particular, analytical expressions for the fringe visibility obtained in a coherent laser interferometric system are presented. An analytical expression for the mean spot radius of a laser beam propagating through an optical system in the presence of tilt and random jitter is obtained. We also consider the propagation of partially coherent light through optical systems. In particular, we derive a generalized van Cittert–Zernike theorem that is valid for an arbitrary optical system that can be characterized by an ABCD ray-transfer matrix. Finally, the propagation of laser beams through a general optical system in the presence of distributed random inhomogeneities is considered. An explicit expression for the mean irradiance distribution of a Gaussian-shaped beam is derived that is valid for an arbitrary optical system. In addition, we derive an expression for the mutual-coherence function for wave propagation through an arbitrary optical system. In all cases the results are expressed in terms of the ABCD matrix elements of the complete optical system. The formulation of optical propagation presented here is a rather simple and straightforward way of determining the effects of finite-sized optical elements, tilt and random jitter, and distributed random inhomogeneities along the optical path. It is merely necessary first to multiply the relevant ray matrices together to find the complete system matrix and then to substitute this matrix into the expressions given in this paper.

Joint Carrier Phase Estimation and Data Detection Algorithms for Multi-h CPM Data Transmission

A dynamic programming algorithm, developed in [1]-[4] for obtaining the joint estimate of carrier phase and data, is applied to multi h continuous phase modulation. A MAP estimator detects data and jointly tracks carrier phase consisting of a normal random walk phase jitter process. Monte Carlo computer simulations are used to evaluate the probability of error performance for two receivers employed in demodulation of multi- h CPM signals. A simplified algorithm is proposed which yields up to a tenfold reduction in computation time at the expense of less than 1 dB in signal-to-noise ratio at the error rates computed, and for suitable ranges of phase jitter increments variance.

Jitter Accumulation for Periodic Pattern Signals

It is important to accurately evaluate and reduce jitter accumulation in long-haul digital repeatered lines. Jitter accumulation caused by random pattern signals has already been analyzed. However, periodic pattern signals such as pseudorandom signals are usually used to measure jitter accumulation. This paper describes the difference between the jitter accumulation for both signals and the necessary conditions to accurately estimate jitter accumulation for random pattern signals by using periodic pattern signals. First, it is shown theoretically that systematic jitter for periodic signals saturates, showing a ripple pattern. The limit of increase is determined by the ratio of tank bandwidth and pattern repetition frequency. Up to a certain number of regenerators determined by the ratio, systematic jitter increases in rough proportion to the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\sqrt{N}</tex> slope. It is also shown that the equation to estimate random pattern jitter accumulation is determined by the measured value for periodic pattern signals. Second, jitter characteristics are simulated by optical signal circulating experiments. The results are in agreement with the analysis. In addition, the reduction effects on periodic signal jitter accumulation caused by timing signal delay and nonlinearity of the limiter in the timing circuit are shown.

Monolithic integrated CMI coder and decoder for gigabit optical links

The high-speed performance of a monolithic integrated CMI coder and decoder, which are fabricated using super self-aligned process technology, is described. The maximum line rate is 3.07 Gbaud. The power consumptions of the coder and decoder are 0.54 W and 0 43 W, respectively. An optical CMI transmission experiment was performed using an InGaAsP/InP laser diode, a Ge APD and an integrated receiver with a SAW filter retiming circuit. When the quality factor Q was 830 at 1.8 Gbaud, random jitter was below 0.7°. In addition, it was confirmed that a clock signal can be extracted from any input data.

A theoretical analysis of the time resolution of a synchroscan streak camera

A statistical method has been developed to treat the phase jitter between the laser pulse and the deflection Signal and the amplitude jitter of the deflection voltage of a synchroscan streak camera. Using normal distribution functions to model these random jitters, an expression for the recorded pulsewidth of a synchroscan streak camera has been obtained. With the aid of this expression, some experimental observations may be explained.

Accumulation of Jitter: A Stochastic Model

A problem that has been considered extensively in the past is the accumulation of jitter in a chain of regenerative repeaters. For simplicity it is usually assumed that all repeaters in the chain are identical. However, this is not the case in real systems, where considerable differences among the repeaters of a chain have been observed. These random variations are due mainly to manufacturing tolerances, aging effects, temperature changes, etc. In this work, we examine the accumulation of systematic and random jitter along the chain, when the repeater transfer functions are subjected to random variations. We derive expressions for the expected value and variance of the output jitter spectrum in terms of average values of the repeater's jitter transfer function. In addition we find the expected value and the variance of the RMS jitter. Finally we examine two special cases where the timing circuit employs either a phased-locked loop or a surface acoustic wave filter, and derive some asymptotic relations for the power spectral density and root-mean-square value of the accumulated systematic jitter.

Jitter accumulation in optical transmission systems

Jitter accumulation on a high-bit-rate submarine optical link has been investigated through signal circulating experiments. One-, 6- and 12-repeater loops exhibit similar accumulation. The variance of the systematic jitter increases as the number of repeaters and the random jitter tends to saturate.

Jitter accumulation with SAW timing extraction at 325 Mbaud

Random, systematic and alignment jitter accumulation on a cascade of 10×325 Mbaud regenerators using SAW timing extraction is described. Good agreement between measurement and theory is shown in each case and a significant advantage over RLC extraction demonstrated.

Contributions of sub‐audio frequency modulation and spectral envelope constancy to spectral fusion in complex harmonic tones

Spectral fusion is a process by which elements of sound are grouped into unified auditory source percepts. The grouping processes use acoustic cues such as the presence of sub‐audio frequency modulation, its coherence among spectral components and the constancy of the spectral envelope. Both periodic (vibrato) and random (jitter) modulation can contribute to fusion. The rms deviation of modulation must be greater than the modulation detection threshold found for these complex tones (16 harmonies of 220 Hz). When the modulation imposed on the ensemble of spectral components is incoherent or does not maintain the harmonic relation (i.e., is not proportional to frequency for all harmonics), less fusion is perceived. There are indications that the detection of coherence of modulation occurs in the higher harmonic numbers. Those modulations which mitigate against fusion also contribute to an increase in spectral resolution. The spectral resolution indicated in these experiments appears to bc greater than that for unmodulated signals classically reported. With more complex spectral envelopes, like vowels, a greater degree of fusion is reported when the spectral envelope is constant, i.e., a concurrent amplitude modulation accompanies frequency modulation and “traces out” the spectral envelope. This may indicate that grouping processes favor fixed‐resonance structures. Musical examples illustrating the use of these principles in computer synthesis will be played.

Temporal discrimination in the goldfish.

The capacities of the goldfish to detect changes in sound burst repetition rate were studied using classical respiratory conditioning. In experiment I, the just detectable amount of an instantaneous random jitter of burst period was measured as a function of mean period. In experiment II, the just detectable amount of slow sinusoidal jitter of burst period was measured for three burst types having different spectral and waveform characteristics. In experiment III, sinusoidal jitter detection thresholds were measured in the presence of varying degrees of random jitter. The data show that (1) rms sinusoidal and random jitter in a periodic train of bursts are approximately equally detectable. (2) Sinusoidal jitter detection depends upon burst period duration and the short-term envelope definition and not upon frequency-domain information. (3) For a given burst period, stimulus jitter and an internal temporal noise appear to add independently to determine period discriminability. (4) Psychophysical estimates of internal temporal noise are 0.160 and 0.710 msec at periods of 5 and 10 msec, respectively. The data are consistent with the hypothesis that the burst period discrimination task is based upon a measurement of the time interval (duration) between spikes in auditory neurons.

Performance of Binary Quantized All Digital Phase-Locked Loop with a New Class of Sequential Filter

Phase-locked loops have been used in various parts of telecommunication systems because of their wide applicability to bit synchronization and FM- and PM-demodulation, etc. Several types of digital phase-locked loops (DPLL's) have also been studied due to the increased reliability and decreased cost of integrated digital circuitry. DPLL's of the type employing binary quantized phase detection and discrete phase adjustments have been utilized for detection of a binary signal or suppression of phase jitter in data-transmission techniques. Unfortunately the width of the locking-range and the ability to suppress phase jitter are contrary to each other, and furthermore, the capacity for jitter suppression rapidly lowers as the frequency of input signal deviates from a free-running frequency of the loop. To improve these vicious properties, a DPLL employing a new type of sequential loop filter is proposed in this paper. The sequential filter controls the properties of itself asymmetrically, depending on the input and output phase distributions to keep the output phase at the center of input phase distribution. The loop performance is analyzed theoretically, experimentally, and by computer simulation in the presence of random Gaussian phase jitter. It is shown that the loop has satisfactory performance as a DPLL used for phase jitter suppression.

An Analysis of Jitter Accumulation in a Chain of PLL Timing Recovery Circuits

This paper analyzes the timing jitter accumulation which is produced in a chain of regenerative repeaters when a second-order phase-locked loop (PLL) is used as a timing filter. In a PLL timing recovery circuit, the growth of timing jitter varies with the value of damping factor \zeta . In this paper, therefore, approximate equations of timing jitter accumulation are given with respect to a case in which \zeta is sufficiently large, and the timing jitter is calculated with a digital computer for various values of \zeta . It is shown that, when \zeta is sufficiently large, results similar to those for first order loops or single tuned circuits are obtained, i.e., the meansquare random jitter is almost proportional to the square root of the number of repeaters, and the mean-square systematic jitter is almost proportional to the number of repeaters. When \zeta is small the meansquare jitter increases exponentially as the number of repeaters is increased. This paper also describes the optimum value of \zeta , considering both the jitter accumulation and the transient response of the PLL, by using the number of repeaters N as a parameter. As a result, it is postulated that the optimum value of \zeta is 5 to 8 when N is 100, and 15 to 18 when N is 1,000.