Harmonic synchronization of nonlinear oscillators

The locking range of a harmonic synchronized oscillator is calculated, and it is shown to be proportional to the relative harmonic amplitude produced by the nonlinearity. For completeness a simple method is given for calculating the harmonic output produced.     

Optical synchronization of millimeter-wave oscillators fordistributed architecture

A review of various methods of phase and frequency synchronization of active MMIC based transmit/receive modules is presented, and particular emphasis is placed on the synchronization of oscillators through the use of an indirect subharmonic optical injection locking technique. In this approach, the nonlinear behavior of large-signal modulated laser diodes and solid-state oscillators is exploited to extend the bandwidth of the synchronizing link to the millimeter-wave frequency range. Experimental results of the phase and frequency coherency of two 21.5 GHz FET oscillators are reported. Optimum performance is achieved at a subharmonic factor of 1/4, with a locking range of 84 MHz and a phase noise degradation of only 14 dB. The phase coherency measurement of two injection-locked oscillators points to a phase shift, which is introduced as a result of the frequency detuning between the slave and master oscillator signals. A scheme to correct for this phase error is presented     

Expected repair cost under doubly stochastic damage processes

There are a number of instances where the problems of non-stationarity, Poisson compounding and double stochasticity arise. In the theory of space-charge limited shot-noise, the number of beats that occur in a given interval of time obey a doubly stochastic process since the Poisson's parameter λ changes randomly due to individual beats. This paper puts forward a doubly stochastic non-stationary compound Poisson process as a model describing damage sustained by military equipment, solar collectors, … etc., due to hailstones. The expected repair cost due to such damage is formulated.     

Antiphase synchronization of chaos in symmetrically coupled self-sustained oscillators

Antiphase chaotic synchronization in symmetrically coupled oscillators with a negative resistance is studied. The domains of existence and stability of synchronous modes are determined. The desynchronization process caused by variation of coupling is considered.     

The threshold of generalized synchronization of chaotic oscillators

The behavior of two unidirectionally coupled chaotic oscillators exhibited at the threshold of generalized chaotic synchronization is considered. The modified-system approach is applied to explain physical mechanisms of formation of this regime in the cases of large and small mismatches of interacting systems.     

Detection of stochastic processes

This paper reviews two streams of development, from the 1940's to the present, in signal detection theory: the structure of the likelihood ratio for detecting signals in noise and the role of dynamic optimization in detection problems involving either very large signal sets or the joint optimization of observation time and performance. This treatment deals exclusively with basic results developed for the situation in which the observations are modeled as continuous-time stochastic processes. The mathematics and intuition behind such developments as the matched filter, the RAKE receiver, the estimator-correlator, maximum-likelihood sequence detectors, multiuser detectors, sequential probability ratio tests, and cumulative-sum quickest detectors, are described     

Transient processes in gunn diodes

The influence of transient processes on the parameters of Gunn logic devices and Gunn generators is considered. For Gunn logic devices the dependence of the switching time on the load resistance R₁ is calculated and the criteria limiting the possible values of $\text{R}{}_1\text{R}{}_0$ (where R₀ is the low field resistance of the Gunn diode) are derived. The simple criterion of the Gunn generation modes is obtained. This criterion allows the prediction of what mode of generation (transit, hybrid or LSA) should take place if the oscillation frequency and the diode parameters are known. For the transit modes in a parallel resonant circuit the change of the resonant frequency due to the diode connection is estimated and the criterion which should be met by the diode parameters and the load resistance is derived. In particular this criterion sets up a limitation of the maximum diode length for the quenched mode at a given frequency. The simple calculation of the basic generation parameters is presented for the case when the Gunn diode operates in a series resonant circuit.     

Synchronization of the assembly of stochastic oscillators in a ring resonator

Dynamics of an “assembly of stochastic oscillators—ring resonator” system is considered via numerical simulation. It is shown that, in systems containing a large number of active elements, self-oscillatory structures are formed. The existence of these structures is related to the capability of interacting elements to retune frequency.     

Transient dynamics of CW intracavity singly resonant opticalparametric oscillators

We study the transient dynamics of CW intracavity, singly-resonant optical parametric oscillators (ICSROs). Relaxation oscillations of the 1064-nm pump light are measured, in both the presence and absence of parametric conversion, in a periodically poled LiNbO₃ (PPLN) CW ICSRO pumped intracavity to a Nd:YVO₄ laser. The presence of parametric conversion is shown to significantly increase both the damping times and oscillation frequencies of the dynamics; at three times the parametric oscillator threshold, these take values of 200 μs and 2 MHz, respectively. Oscillation frequencies are shown to be in good agreement with theoretical values. The influence of energy diffusion and thermal lensing are analyzed to account for discrepences between measured and theoretical damping times. We discuss the implications of the dynamic behavior to the stable-power operation of CW ICSROs     

Semiconductor all-optical modulator for synchronization of independent fiber laser oscillators and active mode-locking

Using an optically driven nonlinear semiconductor mirror, we have synchronized a 1.56-/spl mu/m mode-locked erbium fiber laser to the pulse train from a mode-locked ytterbium fiber laser operating at 1.05 /spl mu/m. We demonstrate that a robust active or passive mode-locked picosecond pulse operation and tight control of the repetition rate can be obtained resulting in a large value of the locking tolerance for the slave laser cavity mismatch exceeding 250 /spl mu/m.     

Alias-free randomly timed sampling of stochastic processes

The notion of alias-free sampling is generalized to apply to random processesx(t)sampled at random timest_n; sampling is said to be alias free relative to a family of spectra if any spectrum of the family can be recovered by a linear operation on the correlation sequence{r(n)}, wherer(n) = E[x(l_{m+n}) overline{x(t_m)}]. The actual sampling timest_nneed not be known to effect recovery of the spectrum ofx(t). Various alternative criteria for verifying alias-free sampling are developed. It is then shown that any spectrum whatsoever can be recovered if{t_n}is a Poisson point process on the positive (or negative) half-axis. A second example of alias-free sampling is provided for spectra on a finite interval by periodic sampling (fort leq t_oort geq t_o) in which samples are randomly independently skipped (expunged), such that the average sampling rate is an arbitrarily small fraction of the Nyquist rate. A third example shows that randomly jittered sampling at the Nyquist rate is alias free. Certain related open questions are discussed. These concern the practical problems involved in estimating a spectrum from imperfectly known{ r(n) }.     

Uncertainty in measurements on spectrally correlated stochastic processes

In this paper, the class of the spectrally correlated stochastic processes is introduced. Processes belonging to this class exhibit a Loe/spl grave/ve (1963) bifrequency spectrum with spectral masses concentrated on a countable set of support curves in the bifrequency plane. Thus, such processes have spectral components that are correlated. The introduced class generalizes the almost-cyclostationary (ACS) processes that are obtained as a special case when the separation between correlated spectral components assumes values only in a countable set. In such a case, the support curves are lines with unit slope. For the spectrally correlated processes, the amount of spectral correlation existing between two separate spectral components is characterized by the bifrequency spectral correlation density function, which is the density of the Loe/spl grave/ve bifrequency spectrum on its support curves. It is shown that, in general, when the location of the support curves is unknown, the time-smoothed cross-periodogram can provide a reliable (low bias and variance) single sample-path-based estimate of the bifrequency spectral correlation density function in those points of the bifrequency plane where the slope of the support curves is not too far from unity. Moreover, there exists a tradeoff between the departure of the nonstationarity from the almost-cyclostationarity and the reliability of spectral correlation measurements obtainable by a single sample-path. Furthermore, in general, the estimate accuracy cannot be improved as wished by increasing the data-record length and the spectral resolution.     

Transient processes in photocathodes at high laser intensities

The transient characteristics of a photocathode observed following the instantaneous onset and termination of optical excitation in one-and two-pulse excitation regimes are considered within a nonlinear diffusion model. The critical values of the illumination intensity corresponding to the manifestation of charge-confinement effects and to the cessation of photoelectron emission are determined. It is shown that the emission charge in a pulse is a nonmonotonic function of the excitation intensity and depends strongly on the values of the negative electron affinity and the effective transparency of the barrier in the activation layer. In the charge-confinement regime the time for establishing a stationary photovoltage and emission current following the onset of excitation is determined mainly by the establishment of equilibrium between the electron and hole fluxes reaching the surface and is inversely proportional to the illumination intensity. The time for restoration of the photocathode characteristics following the termination of illumination is inversely proportional to the trapping rate of holes on deep neutral centers during their tunneling to the surface through the barrier in the space-charge region and can be as large as several microseconds. Fiz. Tekh. Poluprovodn. 32, 1467–1475 (December 1998)     

Transient processes in high-voltage silicon carbide bipolar-junction transistors

The specific features of transient processes in high-voltage silicon carbide bipolar-junction transistors are studied theoretically and experimentally. It is shown that, in good agreement with the experimental results, the switch-off from the active mode can be described in a wide temperature range by the simple analytical expression derived in the study. The process in which a transistor is switched on to pass into the active mode is well described by a simple exponential dependence. The time constant of the switch-on process is determined by the average value of the collector capacitance before and after switch-on. A numerical model is suggested, based on a simple and physically transparent equivalent circuit describing, in good agreement with the experiment, both the transient processes of switch-on and switch-off in a SiC bipolar junction transistor, in both the active and saturation modes.     

A theory of polyspectra for nonstationary stochastic processes

Harmonizable processes constitute an important class of nonstationary stochastic processes. We present a theory of polyspectra (higher order moment spectra) for the harmonizable class. We define and discuss four basic quantities: the nth-order moment function, the nth-order time-frequency polyspectrum, the nth-order ambiguity function, and the nth-order frequency-frequency polyspectrum. The latter generalizes the conventional polyspectrum to nonstationary stochastic processes. These four functions are related to one another by Fourier transforms. We show that the frequency and time marginals of the time-frequency polyspectrum are the instantaneous nth-order moment and the conventional nth-order stationary polyspectrum, respectively. All quantities except the nth-order ambiguity function allow for insightful interpretations in terms of Hilbert space inner products. The inner product picture leads to two novel and very powerful definitions of polycoherence for a nonstationary stochastic process. The polycoherences are objective measures of stationarity to order n, which can be used to construct various statistical tests. Finally, we give some specific examples and apply the theory to linear time-varying systems, which are popular models for fading multipath communication channels.     

Wavelet representations of stochastic processes and multiresolutionstochastic models

Deterministic signal analysis in a multiresolution framework through the use of wavelets has been extensively studied very successfully in recent years. In the context of stochastic processes, the use of wavelet bases has not yet been fully investigated. We use compactly supported wavelets to obtain multiresolution representations of stochastic processes with paths in L² defined in the time domain. We derive the correlation structure of the discrete wavelet coefficients of a stochastic process and give new results on how and when to obtain strong decay in correlation along time as well as across scales. We study the relation between the wavelet representation of a stochastic process and multiresolution stochastic models on trees proposed by Basseville et al. (see IEEE Trans. Inform. Theory, vol.38, p.766-784, Mar. 1992). We propose multiresolution stochastic models of the discrete wavelet coefficients as approximations to the original time process. These models are simple due to the strong decorrelation of the wavelet transform. Experiments show that these models significantly improve the approximation in comparison with the often used assumption that the wavelet coefficients are completely uncorrelated     

Renewal approximations of the doubly stochastic Poisson processes

In this paper, we analyze two approaches to approximate a doubly stochastic Poisson (DSP) process by a renewal process. A DSP process consists of Poisson processes whose rates alternate between two levels. Each rate remains for renewal times forming an alternating renewal process. Such processes can be used to model situations in reliability, inventory, queueing and production systems. We develop two expressions for the Laplace-Stieltjes transforms of the interrenewal time distributions of the renewal processes that approximate a DSP process. We then use these approximations to develop expressions for the stationary loss probability in a G/M/1/0 system. We evaluate the quality of these approximations by comparing them against exact results. Our approximations should be of significant use in several practical applications.     

Transient response of an infinite cylindrical antenna in a dissipative medium

The transient solution of an infinite cylindrical antenna in a dissipative medium caused by an impulse excitation at a delta gap is obtained via an exact solution in the form of definite integrals and a simple asymptotic formula. This formula is used to obtain an integral for calculating the antenna current caused by a double exponential input voltage at the gap; furthermore, the resulting integral reduces to Sunde's classic result under the diffusion limit. These results are applied to the transient response of a buried wire subject to an electromagnetic pulse (EMP) or nearby lightning incident wave.     

Transient processes in an oscillatory circuit caused by stepwise phase changes

Transient processes at the output of an isolated oscillatory circuit caused by stepwise phase changes at the circuit input are studied in the time and frequency domains. A mathematical model of this type of transient processes in the form of a narrowband process is presented. Analytical expressions describing the behavior of the transient process in the time and frequency domains are obtained. New features of this type of transient processes are revealed.     

Transient processes in a bandpass filter caused by stepwise phase variations

Transient processes at the output of a bandpass filter caused by a stepwise phase variation in the input high-frequency signal are studied in the time domain. A mathematical model of this type of transient processes in the form of a narrowband process is presented. Analytic expressions describing the behavior of the transient process in the time domain are obtained. New features of this type of transient processes are revealed.