Benefits from a speckle noise family on a coherent imaging transmission

We analyze image transmission in a coherent imaging system, in the presence of speckle noise modeled with the family of Gamma probability density functions of varying order. It is demonstrated that speckle noise can improve the transmission of a coherent image. Exact analytical expressions are obtained for both the best achievable performance and the optimal amount of speckle noise maximizing the transmission efficacy. These expressions allow us to analyze and control the conditions under which the coherent imaging system can take advantage of the speckle noise. The influence of the contrast in the coherent image, and of the order of the Gamma probability density describing the statistical fluctuations of the speckle, are given special attention. These results make a contribution to the understanding of the mechanisms of improvement by noise in nonlinear information processing.     

Improved analysis of dispersion penalty in optical fibre systems

Based on the model presented by Campbell [1], simple and convenient formulae are developed for calculating the dispersion penalty with consideration of the system pulse shaping, the laser diode spectrum and the different statistics of mode partition noise within and between baud periods. Numerical calculations show that they are good approximations of the complex expressions given by Campbell. Furthermore, we show that Ogawa's mode partition noise expressions in [2] should be corrected by a factor of about 2 and the wave shape at decision should be carefully designed to minimize the mode partition noise.     

水下目标对幅度高斯相关海面环境噪声场扰动特性的研究

理论探讨了水下目标受海面环境噪声场激发产生的散射场对海洋环境噪声场的扰动特性,基于幅度高斯型相关海面噪声源模型,利用任意声源分布声场的积分表达式和单极子源半无限空间格林函数的球面波展开式,获得了刚性球目标在海面单极子和偶极子源海洋环境噪声“照射”下的直达噪声场、散射噪声场、总噪声场,以及二接收点直达、散射和总噪声协方差的理论表达式,表明总噪声场除了和目标阻抗特性、接收点的方向有关外,还受到海面噪声源相关特性,以及直达与散射噪声场之间干涉的较大影响。数值计算结果给出较近距离范围内,刚球目标声学可见度约为4~5dB,并指出在海洋环境噪声场中,刚球目标散射的方向特性明显不同于平面波入射。      

The study on a stochastic system with non-Gaussian noise and Gaussian colored noise

In this paper, a stochastic system with correlation between non-Gaussian noise and Gaussian colored noise is investigated. We carry out the functional methods to derive the approximate Fokker-Planck equation, and the expressions of stationary probability density function and mean first-passage time are presented. Also we explore the effects of correlation between non-Gaussian and Gaussian noise for the mean first-passage time.     

Lyapunov number for a noisy 2 n cycle

A stochastic one-dimensional map which produces a sequence of period doubling bifurcations is theoretically studied. We obtain analytic expressions, to a second-order approximation, of the local distribution function of fluctuating orbital points and the Lyapunov number for a noisy 2 ⁿ cycle. The expressions satisfy scaling laws and well agree with the results of numerical experiments when the external noise is weak. A scaling factor for the noise level is formulated in terms of the derivatives of a deterministic map. From it, the scaling factor is refined to be 6.6190 .... The Lyapunov number shows that, when the external noise is weaker than some extent, the noisy orbit is more stable rather than the deterministic one.     

Background noise in piezoresistive,electret condenser,and ceramic microphones

Background noise studies have been extended from air condenser microphones to piezoresistive, electret condenser, and ceramic microphones. Theoretical models of the respective noise sources within each microphone are developed and are used to derive analytical expressions for the noise power spectral density for each type. Several additional noise sources for the piezoresistive and electret microphones, beyond what had previously been considered, were applied to the models and were found to contribute significantly to the total noise power spectral density. Experimental background noise measurements were taken using an upgraded acoustic isolation vessel and data acquisition system, and the results were compared to the theoretically obtained expressions. The models were found to yield power spectral densities consistent with the experimental results. The measurements reveal that the 1/f noise coefficient is strongly correlated with the diaphragm damping resistance, irrespective of the detection technology, i.e., air condenser, piezoresistive, etc. This conclusion has profound implications upon the expected 1/f noise component of micromachined (MEMS) microphones.     

Cramér-Rao Bound Expressions for Parametric Estimation of Overlapping Peaks: Influence of Prior Knowledge

We have derived analytical expressions of the Cramér-Rao lower bounds on spectral parameters for singlet, doublet, and triplet peaks in noise. We considered exponential damping (Lorentzian lineshape) and white Gaussian noise. The expressions, valid if a sufficiently large number of samples is used, were derived in the time domain for algebraic convenience. They enable one to judge the precision of any unbiased estimator as a function of the spectral and experimental parameters, which is useful for quantitation objectives and experimental design. The influence of constraints (chemical prior knowledge) on parameters of the peaks of doublets and triplets is demonstrated both analytically and numerically and the inherent benefits for quantitation are shown. Our expressions also enable analysis of spectra comprising many peaks.     

Fractionalization noise in edge channels of integer quantum Hall states

A theoretical calculation is presented of current noise which is due charge fractionalization, in two interacting edge channels in the integer quantum Hall state at filling factor ν=2. Because of the capacitive coupling between the channels, a tunneling event, in which an electron is transferred from a biased source lead to one of the two channels, generates propagating plasma mode excitations which carry fractional charges on the other edge channel. When these excitations impinge on a quantum point contact, they induce low-frequency current fluctuations with no net average current. A perturbative treatment in the weak tunneling regime yields analytical integral expressions for the noise as a function of the bias on the source. Asymptotic expressions of the noise in the limits of high and low bias are found.     

Characteristics of the Phase Noise Correlation of Injection Locked Lasers for RF Signal Generation and Transmission

Theoretical and experimental results on phase noise characteristics of an optical radio-frequency generation and transmission system using heterodyne photo-detection and side band injection locking is reported. Optical phase noise correlation of the lasers is achieved by noise transfer from a modulated master laser. Our investigation takes into account phase noise enhancement in optical comb generation, injection dynamic, path delay, and fiber dispersion. Theoretical expressions are derived from an adiabatic approximation and compared with experimental measures.     

Tests of numerical simulation algorithms for the Kubo oscillator

Numerical simulation algorithms for multiplicative noise (white or colored) are tested for accuracy against closed-form expressions for the Kubo oscillator. Direct white noise simulations lead to spurious decay of the modulus of the oscillator amplitude. A straightforward colored noise algorithm greatly reduces this decay and also provides highly accurate results in the white noise limit.     

A model for spatial coherence from directive ambient noise in attenuating, dispersive media

As a complement to experimental efforts in seismics and acoustics to infer geo-acoustic properties of the propagation environment from the second order statistics of ambient noise measurements, a set of exact, explicit, closed form expressions for the cross-spectral density and spatial coherence of diffuse random wave fields is presented. Taken together, the expressions are well suited for modeling broadband, diffuse wave coherence in realistic scenarios involving directive, ambient noise from local (i.e., volume) and distant (i.e., plane wave) source features in an open, dispersive, attenuating medium.     

Nonadiabatic electron pumping: maximal current with minimal noise

The noise properties of pump currents through an open double-quantum-dot setup with nonadiabatic ac driving are investigated. Driving frequencies close to the internal resonances of the double-dot system mark the optimal working points at which the pump current assumes a maximum while its noise power possesses a remarkably low minimum. A rotating-wave approximation provides analytical expressions for the current and its noise power and allows to optimize the noise characteristics. The analytical results are compared to numerical results from a Floquet transport theory.     

Analysis of signal-to-noise enhancement of box-car averagers

The signal-to-noise improvement ratio (SNIR) of a Box-Car averager is calculated for various noise sources such as random white noise, exponentially correlated noise, etc. For a time constant (RC), and a sampling time ε, the quoted value of SNIR as (2RC/ε)^1/2 is shown to be strictly correct only when the noise is white and deviation from this law is expected for other non-white noise sources. The validity of some of the calculated expressions is established by direct measurement of noise output.     

Study of the influence of phase fluctuations on the characteristics of an OFDM radio-communication system

We consider the influence of phase fluctuations on the operation characteristics of an OFDM radio-communication system. We present the results of studying the effect of additional nonorthogonality noise appearing after the fast Fourier transform due to the phase noise and frequency detuning between the receiver and transmitter oscillators. Approximate analytical expressions for the power of additional nonorthogonality noise are presented for the classical Lorentzian model of the phase noise. Degradation of the signal-to-noise ratio in the OFDM radio-communication system is studied and analytical expressions are given for calculation of this quantity as a function of the frequency detuning and half-width of the spectral line of an oscillator. We present the computer simulation results con.rming the analytical evidence. Based on the obtained results, recommendations for practical choice of the parameters of an OFDM radio-communication system can be given. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 50, No. 2, pp. 169–180, February 2007.     

Estimation of increases in noise levels due to installation of transverse rumble strips on urban roads

Increases in noise due to the installation of transverse rumble strips were investigated, by first measuring noise due single vehicles crossing a pilot test field with and without a rumble strip. After that, a procedure was proposed and carried out to estimate increases in noise due to the traffic of vehicles, based on the measurements previously mentioned. This procedure was checked against expressions from the literature that estimate traffic noise as well as measurements in three arterial urban roads without rumble strips installed. Its accuracy was compatible with the ones obtained by applying the literature expressions, the errors lying below 3 dB(A). Then, by taking the aforementioned roads as case studies, estimations were carried out for the increases that would occur in noise levels if rumble strips were installed on them, leading to values between 6 and 7 dB(A). Although such values are dependent on the configuration of the rumble strip employed, the proposed procedure presents generality and could be applied to estimate increases in traffic noise due to installation of rumble strips, by departing from measurements of noise due to single vehicles obtained for a given rumble strip configuration.     

Analytical expressions for the intensity and frequency noise of an individual mode in a multimode semiconductor laser with external optical feedback

Analytical expressions are derived for the intensity and frequency noise of each individual mode in a multimode semiconductor laser with external optical feedback. It is shown that in a two-mode laser the side-mode effect on the intensity noise is enhanced by the optical feedback which gives the maximum linewidth narrowing.     

Stochastic resonance in a bias linear system with multiplicative and additive noise

In this paper, the stochastic resonance in a bias linear system subjected multiplicative and additive dichotomous noise is investigated. Using the linear-response theory and the properties of the dichotomous noise, this paper finds the exact expressions for the first two moments and the signal-to-noise ratio (SNR). It is shown that the SNR is a non-monotonic function of the correlation time of the multiplicative and additive noise, and it varies non-monotonously with the intensity and asymmetry of the multiplicative noise as well as the external field frequency. Moreover, the SNR depends on the system bias, the intensity of the cross noise between the multiplicative and additive noise, and the strength and asymmetry of the additive noise.     

Raman-noise-induced noise-figure limit for chi(3) parametric amplifiers

The nonzero response time of the Kerr [chi(3)] nonlinearity determines the quantum-limited noise figure of chi(3) parametric amplifiers. This nonzero response time of the nonlinearity requires coupling of the parametric amplification process to a molecular-vibration phonon bath, causing the addition of excess noise through Raman gain or loss at temperatures above 0 K. The effect of this excess noise on the noise figure can be surprisingly significant. We derive analytical expressions for this quantum-limited noise figure for phase-insensitive operation of a chi(3) amplifier and show good agreement with published noise-figure measurements.     

Stochastic resonance in linear system driven by multiplicative and additive noise

The stochastic resonance (SR) is studied in an overdamped linear system driven by multiplicative and additive noise when the additive noise is a linear combination of an asymmetric dichotomous noise and its square. The exact expressions are obtained for the first two moments and the correlation function and the SR phenomenon appeared. There are three different forms of SR: the bona fide SR, the conventional SR and SR in the broad sense. Moreover, the asymmetry of multiplicative noise has different effect on signal-to-ratio (SNR) for the first two different forms of SR and the effects of multiplicative noise and additive noise on SNR are different.