Bootstrapping the Local Periodogram of Locally Stationary Processes

Abstract. Locally stationary processes are non‐stationary stochastic processes the second‐order structure of which varies smoothly over time. In this paper, we develop a method to bootstrap the local periodogram of a locally stationary process. Our method generates pseudo local periodogram ordinates by combining a parametric time and non‐parametric frequency domain bootstrap approach. We first fit locally a time varying autoregressive model so as to capture the essential characteristics of the underlying process. A locally calculated non‐parametric correction in the frequency domain is then used so as to improve upon the locally parametric autoregressive fit. As an application, we investigate theoretically the asymptotic properties of the bootstrap method proposed applied to the class of local spectral means, local ratio statistics and local spectral density estimators. Some simulations demonstrate the ability of our method to give accurate estimates of the quantities of interest in finite sample situations and an application to a real‐life data‐set is presented.     

Variations in Spectral Slope in Lake Taihu,a Large Subtropical Shallow Lake in China

Spectral slope (S), describing the exponential decrease of the absorption spectrum over a given wavelength range, is an important parameter in the study of of chromophoric dissolved organic matter (CDOM) dynamics, and also an essential input parameter in remote sensing models. Furthermore, S is often used as a proxy for CDOM composition, including the ratio of fulvic to humic acids and molecular weight. The relative broad range in S values reported in the literature can be explained by the different spectral ranges and fitting methods used. A single exponential model is used to fit the S values for 17 investigations involving 458 samples in Lake Taihu from January to October in 2004. The average S value was 15.18 ± 1.39 μm⁻¹ for the range of 280–500 nm, which fell within the range reported in the literature. The frequency distribution of S value basically obeyed a normal distribution. Significant differences in S values between summer and other seasons showed that phytoplankton degradation was one of the important sources of CDOM in summer, whereas CDOM mainly came from the river input in other seasons. Furthermore, the estimated S value decreased with increasing wavelength range used in regression. The maximum and minimum values derived from the regression were 17.89 ± 1.25 μm⁻¹ and 13.62 ± 2.11 μm⁻¹ for the wavelength ranges of 280–380 nm and 400–500 nm, respectively, a decrease of 23.9%. S values significantly decreased with the increase of CDOM absorption coefficients. CDOM absorption coefficients could be more appropriately estimated from exponential model introducing the variation of S with absorption coefficients, making them useful for a remote sensing bio-optical model of Lake Taihu. DOC-specific absorption coefficient a*(λ) and the parameter M describing molecular size of the humic molecules could also be used as a proxy for the sources and types of CDOM. A general relationship was found between S and a*(λ), and M values. S increased with the decrease of DOC-specific absorption coefficient and the increase of M corresponding to the decrease of molecular weight.     

New method for measuring an optical property of a sample treated by FWA

In this article, a new method for measuring a total spectral radiance factor of a FWA‐treated sample illuminated by a specific standard illuminant is introduced. The method replaces an unstable real fluorescent standard by a bi‐spectral luminescent radiance factor data, which works as a virtual fluorescent standard (VFS) by knowing spectral intensity distributions of illuminations applied to the sample. The method utilizes two illuminations I₁ and I₂ whose relative spectral intensity distributions are different from each other and synthesizes a virtual illumination presenting the identical fluorescent spectral radiance factor to that presented by the standard illuminant with the VFS of the specific bi‐spectral luminescent radiance factor by linearly combining I₁ and I₂ with the suitable weighting factors. The applicability of the method is examined in principle by comparing ISO brightness and CIE whiteness index of fluorescent standard paper as a test sample obtained by this new method to the assigned values. © 2007 Wiley Periodicals, Inc. Col Res Appl, 32, 195–200, 2007     

Spectral color reproduction minimizing spectral and perceptual color differences

In this article, we are combining minimization criteria in the colorant separation process for spectral color reproduction. The colorant separation is performed by inverting a spectral printer model: the spectral Yule‐Nielsen modified Neugebauer model. The inversion of the spectral printer model is an optimization operation in which a criterion is minimized at each iteration. The approach we proposed minimizes a criterion defined by the weighted sum of a spectral difference and a perceptual color difference. The weights can be tuned with a parameter α ∞ [0, 1]. Our goal is to decrease the spectral difference between the original data and its reproduction and also to consider perceptual color difference under different illuminant conditions. In order to find the best α value, we initially compare a pure colorimetric criterion and a pure spectral criterion for the reproduction, then we combine them. We perform four colorant separations: the first separation will minimize the 1976 CIELAB color difference where four illuminants are tested, the second separation will minimize an equally weighted summation of 1976 CIELAB color difference with the four illuminants tested independently, the third colorant separation will minimize a spectral difference, and the fourth colorant separation will combine a weighted sum of a spectral difference and one of the two first colorimetric differences previously introduced. This last colorant separation can be tuned with a parameter in order to emphasize on spectral or colorimetric difference. We use a six colorants printer with artificial inks for our experiments. The prints are simulated by the spectral Yule‐Nielsen modified Neugebauer model. Two groups of data are used for our experiments. The first group describes the data printed by our printing system, which is represented by a regular grid in colorant space of the printer and the second group describes the data which is not originally produced by our printing system but mapped to the spectral printer gamut. The Esser test chart and the Macbeth Color Checker test chart have been selected for the second group. Spectral gamut mapping of this data is carried out before performing colorant separation. Our results show improvement for the colorant separations combining a sum of 1976 CIELAB color difference for a set of illuminants and for the colorant separation combining a sum of 1976 CIELAB color difference and spectral difference, especially in the case of spectral data originally produced by the printer. © 2008 Wiley Periodicals, Inc. Col Res Appl, 33, 494–504, 2008     

Spectral approximations of the Stokes problem by divergence-free functions

The method of Moser, Moin, and Leonard (1983) for the approximation of the three-dimensional Navier-Stokes equations using divergence-free subspaces is revisited and analyzed. It is shown that the computed velocity field converges to the physical one with spectral accuracy. Moreover, a method for recovering the pressure field is proposed. This method is stable and provides a pressure that converges to the physical one with spectral accuracy.     

An analytical and numerical study of the two-dimensional Bratu equation

Bratu's problem, which is the nonlinear eigenvalue equationu+ exp(u)=0 withu=0 on the walls of the unit square and as the eigenvalue, is used to develop several themes on applications of Chebyshev pseudospectral methods. The first is the importance ofsymmetry: because of invariance under the C₄ rotation group and parity in bothx andy, one can slash the size of the basis set by a factor of eight and reduce the CPU time by three orders of magnitude. Second, the pseudospectral method is ananalytical as well as a numerical tool: the simple approximation3.2A exp(–0.64A), whereA is the maximum value ofu(x, y), is derived via collocation with but a single interpolation point, but is quantitatively accurate for small and moderateA. Third, the Newton-Kantorovich/Chebyshev pseudospectral algorithm is so efficient that it is possible to compute good numerical solutions—five decimal places—on amicrocomputer inbasic. Fourth, asymptotic estimates of the Chebyshev coefficients can be very misleading: the coefficients for moderately or strongly nonlinear solutions to Bratu's equations fall off exponentially rather than algebraically withv untilv is so large that one has already obtained several decimal places of accuracy. The corner singularities, which dominate the behavior of the Chebyshev coefficients in thelimit v, are so weak as to be irrelevant, and replacing Bratu's problem by a more complicated and realistic equation would merely exaggerate the unimportance of the corner branch points even more.     

光源谱宽通过光纤色散对AOCS输出的影响

基于光纤色散引起的脉冲展宽效应,在理论和实验上研究了有源光学电流传感器（AOCS）中宽带光源对系统输出的影响．理论结果表明：对于长度为500m的光纤,当光源谱宽在40—60nm之间变化时,多模光纤传输下的脉冲展宽范围在0．5～0．8ns,单模光纤传输下的脉冲展宽范围在2×10^-5～4×10^-5,信号衰减量对系统输出影响很小,且随光源谱宽的增加而有微弱的增加,实验与理论相符合．     

高速超宽带系统中频谱优化方法的研究

脉冲波形设计和频谱控制是超宽带通信系统解决频谱共存和相互干扰问题的关键。提出了基于最小面积准则(LAC)的频谱优化方法,并将其应用在正交脉冲调制超宽带系统中。该系统由多条并行发送支路组成,每条支路利用正交脉冲进行脉冲位置调制(PPM)与脉冲形状调制(PSM)相结合的调制。仿真结果表明:利用LAC优化的结果和最小均方误差准则(MMSE)相比更符合FCC的要求,不仅能提高频谱利用率,还能实现对频谱的灵活控制。     

基于改进的Capon滤波器组谱估计新方法

为了解决Capon滤波器组谱估计方法在α稳定分布噪声下性能出现退化的问题,提出了一种改进的Capon滤波器组谱估计方法,利用分数低阶协方差(FLOC)对传统的Capon滤波器组进行重构.由于分数低阶协方差的作用范围是0＜α≤2整个分数低阶空间,因此在α稳定分布噪声下其谱估计性能比基于二阶统计量方法的谱估计性能更好.计算机仿真结果显示了这种方法的优越性能,并且在高斯噪声环境下,其性能与二阶统计量下的方法类似.