Recursive approximation of the energy spectral density

In a previous paper, R.Z. Kham et al. (ibid., vol.35, p.102-5, Jan. 1988) described a fast technique for estimating the energy spectral density of a noisy waveform via Taylor series. A fast sliding-time window approach for recursively updating the series is introduced in this work. A method for automatically determining the required series degree using the estimated truncation error is given. The application of the method is demonstrated in an example. The technique is shown to be more efficient than interpolation of the DFT modulus     

Calculation of Doppler spectral power density functions

A volume integral method for the calculation of Doppler ultrasound spectral power density (spd) functions is described. Axisymmetric flow in a circular tube with a power law velocity profile is assumed. The spd function is regarded as a probability density function for scatterer velocity, and the assumptions under which this is justified are considered. It is shown that the spd function is independent of Doppler angle except in the presence of wall reflection effects. A coordinate system centered on the beam is used and this enables the integrals to be easily formulated for arbitrary beams. Irregularly shaped and nonuniform beams can be treated. For the common flow and beam patterns, which exhibit symmetry, the volume integrals can often be reduced to a single integral and evaluated directly. The method is applied and the spectra are calculated for various different cases. Results are obtained for uniform rectangular and circular insonating beams, and for nonuniform beams with Gaussian, jinc, and sinc profiles. The effects of narrow beams and wall reflection are shown. The method may be readily applied to other beam and flow patterns, and extension to more complicated situations is also discussed.     

基于FFT计算a平稳过程概率密度的改进算法

在网络流量建模和参数估计的过程中,α平稳过程的概率密度计算是一项重要的基础工作。结合α平稳过程特征函数的数学特性,在以往基于FFT求解α平稳过程概率密度函数算法的基础上做出如下改进：通过计算自动选择合适的采样区间和采样间隔;引入扩频进一步降低计算复杂度。实验表明,改进算法比传统算法计算复杂度更低,并可以有效控制计算误差。     

Power spectral density of on-off sources

A closed-form expression is derived for the power spectral density of the traffic generated by a broad class of on-off sources. An example illustrates the use thereof in studying the correlation structure of the traffic process, focusing on the distinction between short- and long-range dependence     

A single-frequency approximation for interface-state density determination

Fast interface state densities in the SiSi₂ system can be determined by measurements of the MIS capacitor admittance. Traditional detailed analysis require elaborate frequency dependent techniques. The more commonly used approximation techniques are difficult to interpret for interface state densities less than 1 × 10¹¹ eV^?1 cm^?2. We present here a new single frequency technique as an approximation method which provides quantitative criteria on the quality of such interfaces. The data required are a single high frequency capacitance vs voltage measurement and a corresponding conductance vs voltage measurement. The validity of this technique is best demonstrated in a three-dimensional plot of conductance, frequency and voltage. This also gives added insight into the relationship between the temporal and thermodynamic properties of interface electronic states. Comparison of results using this approximation to more detailed treatments demonstrates the validity of this new method for low surface state density determination in a range from 7 × 10⁹ eV^?1 cm^?2 to 8 × 10¹¹ eV^?1 cm^?2.     

Numeric approximation of Bessel functions using the DFT

It is well known that the sideband amplitudes of a single-tone frequency-modulated carrier are of the form Jn(B), where B is the modulation index. By selecting appropriate frequency relationships between the sample frequency and the carrier and modulation frequencies, the DFT can be used to calculate Jn(B) with reasonable accuracy.     

Probability density functions of soft information

It is well known that soft decoding algorithms are based on the use of reliability measures for binary and nonbinary symbols. We consider an analytical estimation of the distributions of reliability measures after soft decoding of block and convolutional codes or intersymbol interference (ISI) channels. This estimation, based on a simple geometric interpretation of reliability measures, allows the observation of different distributions for correct and incorrect symbols, and could be helpful for the analysis of soft decoding algorithms     

Approximation of distribution and density functions

Stochastic approximation algorithms are used to construct least squares error approximations to density and distribution functions. The approximation is linear in terms of the parameters to be estimated. The only information available to the algorithm is a sequence of independent samples from the distribution of density being approximated.     

光学表面功率谱密度的表征

以硅基板镀制单层HfO2薄膜前后的表面微观形貌的变化为例,开展了光学表面功率谱密度的计算及表征研究。首先给出了一维功率谱密度(PSD1D)、二维功率谱密度(PSD2D)以及各向同性功率谱密度(PSDISO)的计算方法和具体步骤。然后使用原子力显微镜测量了硅基板镀膜前后在1 m1 m、5 m5 m、10 m10 m、20 m20 m四种扫描尺寸下的表面轮廓。在此基础上使用MATLAB编程计算得到这四种扫描尺寸下的PSDISO,对这些PSDISO使用几何平均算法拼接得到具有足够大频率范围的PSDISO-Combined。结果显示,硅基板镀膜前后的PSDISO-Combined在低频段基本相同,中高频段出现了明显差异。分析指出这是由镀膜后表面柱状晶体结构引起的。提出了对PSDISO在频域上积分得到表面均方根粗糙度ISO,再同由定义式计算得到的STD作对比的方法。计算得到的ISO与STD基本相同,验证了PSDISO计算方法的准确性。     

A uniform power spectral density jamming signal

In this work a technique is described for generating a jamming signal with a continuous uniform-power-spectral density band-limited over any desired frequency band. Experimental results demonstrating the technique are presented.     

Power spectral density bounds (Corresp.)

The determination of a power density spectrum from a finite set of correlation samples is an ill-posed problem. Furthermore. it is not possible even to bound the values that consistent power density spectra can take on at a particular point. A more reasonable problem is to try to determine the total spectral power in some frequency interval. Although this power cannot be determined exactly, upper and lower bounds on its possible values can be determined. This observation leads to a unified treatment of certain classical and modern spectral estimation techniques and to new interpretations for two data adaptive spectral estimators. maximum likelihood method (MLM) and data adaptive spectral estimator (DASE). According to these new interpretations. MLM and DASE provide upper bounds on spectral power in a specified frequency region subject to the assumption that the spectral density is constant in that region. These methods make no use of an extendibility constraint that can be used to obtain tight upper bounds, as well as nontrivial lower bounds on power. Cybenko has studied a related problem of bounding windowed power, for an arbitrary window, with no assumptions about the form of the spectral density. A new type of classical resolution limit for these bounds is derived and a numerical example is presented.     

Power spectral density estimation via wavelet decomposition

A soft decision algorithm for wavelet decomposition, in which a probability measure is assigned to each frequency band bearing energy, is presented. This soft decision algorithm is used as an approximate estimator of power spectral density. A staircase approximation of power spectral density (PSD) is obtained by plotting the 2/sup m/ probabilities after an m-stage decomposition. Different wavelet filters are used for estimating the PSD of a speech segment. The type of the wavelet filter used can be selected as a compromise between accuracy and complexity.     

Estimation of probability density function using spectral analysis

The authors present a new bound on the estimation of the probability density function of random signals, using Woodward's theorem, correlation techniques and spectral analysis. The proposed method is based on the spectral analysis of the random process     

Reduction of spectral noise density in p-i-n-HEMT lightwavereceivers

The spectral noise density of a lightwave receiver is computed from known physical parameters of the photodiode and the high-electron-mobility transistor (HEMT). Low noise is achieved for an appropriate choice of device parameters. The results are applied to circuits built with readily available commercial HEMTs and p-i-n photodiodes. They also predict the superior noise performance of cooled receivers which cannot be readily derived from previous work     

Goodness-of-fit tests based on Kullback-Leibler discriminationinformation

We present a general methodology for developing asymptotically distribution-free goodness-of-fit tests based on the Kullback-Leibler discrimination information. The tests are shown to be omnibus within an extremely large class of nonparametric global alternatives and to have good local power. The proposed test procedure is a nonparametric extension of the classical Neyman-Pearson log-likelihood ratio test and is based on mth-order spacings between order statistics cross-validated by the observed log likelihood. The developed method also generalizes Cox's procedure of testing separate families and covers virtually all parametric families of distributions encountered in statistics. It can also be viewed as a procedure based on sum-log functionals of nonparametric density-quantile estimators cross-validated by the log likelihood. With its good power properties, the method provides an extremely simple and potentially much better alternative to the classical empirical distribution function (EDF)-based test procedures. The important problem of selecting the order of spacings m in practice is also considered and a method based on maximizing the sample entropy constrained by the observed log likelihood is proposed. This data driven method of choosing m is demonstrated by Monte Carlo simulations to be more powerful than deterministic choices of m and thus provides a practically useful tool for implementing our test procedure     

压控振荡器功率谱密度的研究

本文在分析计算了压控振荡器电路中的输出功率谱密度的基础上,针对控制电压涨落的情况,求解了振荡频率随机时的朗之万（Ｌａｎｇｅｖｉｎ）方程,获得了振荡频率涨落的均方根（ｒｍｓ）值,给出了涨落－耗散定理的一种表述,这使我们能更好地研究功率谱密度的线宽和有关噪声的起源。     

Goodness-of-fit tests based on Kullback-Leibler information

We evaluate the power of the sample entropy goodness-of-fit tests for s-normal, exponential, and uniform distributions. We compare them with the mainstream statistical tests, the W test based on the best linear unbiased estimator (BLUE) of the location parameter, the Z test based on the sample spacings, and the R test based on the correlation coefficient between the order statistics of the sample & the corresponding population quantiles. We show that the latter are more powerful overall. The mainstream statistical tests, particularly the Z test, readily extend to censored samples and to multi-sample situations.     

Probability density functions of amplitude-modulated random signals

The probability density function arising from multiplication of two independent random variables has been extensively treated by statisticians, yet some common signal processing product situations have not been analysed. An important example of this omission is the amplitude modulation of a Gaussian process. Here, a little-known Hankel transform-based procedure provides a ready solution for this problem and many other types of random modulation signals. Several new modulation results are tabulated in graphical form and it is also shown that half-amplitude sinusoidal processes added yield the same distribution as their (unit-amplitude) product