Spectral moments from the ACF or directly from the signal

The moments of a bandlimited power spectrum can be estimated from samples of the autocorrelation function without computing the spectrum. Further, short-time estimates of the moments can be continually formed directly from the signal, circumventing ACF computation. Such fast moment computation is of interest in EEG analysis.     

Nonparametric estimation of mean Doppler and spectral width

This paper proposes a new nonparametric method for estimation of spectral moments of a zero-mean Gaussian process immersed in additive white Gaussian noise. Although the technique is valid for any order moment, particular attention is given to the mean Doppler (first moment) and to the spectral width (square root of the centered second spectral moment). By assuming that the power spectral density (PSD) of the underlying process is bandlimited, the maximum-likelihood estimates of its spectral moments are derived. A suboptimal estimate based on the sample covariance is also studied. Both methods are robust in the sense that they do not rely on any assumption concerning the PSD (besides being bandlimited). Under weak conditions, the set of estimates based on sample covariance is unbiased and strongly consistent. Compared with the classical pulse pair and the periodogram-based estimators, the proposed methods exhibit better statistical properties for asymmetric spectra and/or spectra with large spectral widths, while involving a computational burden of the same order     

Moments of a filtered binary process (Corresp.)

The problem of determining the moments of the output of a resistance-capacitance (RC) filter driven by a random binary process is considered. It is assumed that the driving process is governed by an alternating renewal process. A method is given for computing the moments of any order, as well as the conditional moments and moments of the local maxima and minima. Explicit formulas are given for the second moment in the asymmetric case and second and fourth moments in the symmetric case.     

Image analysis by Gaussian-Hermite moments

Orthogonal moments are powerful tools in pattern recognition and image processing applications. In this paper, the Gaussian-Hermite moments based on a set of orthonormal weighted Hermite polynomials are extensively studied. The rotation and translation invariants of Gaussian-Hermite moments are derived algebraically. It is proved that the construction forms of geometric moment invariants are valid for building the Gaussian-Hermite moment invariants. The paper also discusses the computational aspects of Gaussian-Hermite moment, including the recurrence relation and symmetrical property. Just as the other orthogonal moments, an image can be easily reconstructed from its Gaussian-Hermite moments thanks to the orthogonality of the basis functions. Some reconstruction tests with binary and gray-level images (without and with noise) were performed and the obtained results show that the reconstruction quality from Gaussian-Hermite moments is better than that from known Legendre, discrete Tchebichef and Krawtchouk moments. This means Gaussian-Hermite moment has higher image representation ability. The peculiarity of image reconstruction algorithm from Gaussian-Hermite moments is also discussed in the paper. The paper offers an example of classification using Gaussian-Hermite moment invariants as pattern feature and the result demonstrates that Gaussian-Hermite moment invariants perform significantly better than Hu's moment invariants under both noise-free and noisy conditions.     

Surface Roughness and Critical Exponent Analyses of Boron-Doped Diamond Films Using Atomic Force Microscopy Imaging: Application of Autocorrelation and Power Spectral Density Functions

The evolution of the surface roughness of growing metal or semiconductor thin films provides much needed information about their growth kinetics and corresponding mechanism. While some systems show stages of nucleation, coalescence, and growth, others exhibit varying microstructures for different process conditions. In view of these classifications, we report herein detailed analyses based on atomic force microscopy (AFM) characterization to extract the surface roughness and growth kinetics exponents of relatively low boron-doped diamond (BDD) films by utilizing the analytical power spectral density (PSD) and autocorrelation function (ACF) as mathematical tools. The machining industry has applied PSD for a number of years for tool design and analysis of wear and machined surface quality. Herein, we present similar analyses at the mesoscale to study the surface morphology as well as quality of BDD films grown using the microwave plasma-assisted chemical vapor deposition technique. PSD spectra as a function of boron concentration (in gaseous phase) are compared with those for samples grown without boron. We find that relatively higher boron concentration yields higher amplitudes of the longer-wavelength power spectral lines, with amplitudes decreasing in an exponential or power-law fashion towards shorter wavelengths, determining the roughness exponent (α ≈ 0.16 ± 0.03) and growth exponent (β ≈ 0.54), albeit indirectly. A unique application of the ACF, which is widely used in signal processing, was also applied to one-dimensional or line analyses (i.e., along the x- and y-axes) of AFM images, revealing surface topology datasets with varying boron concentration. Here, the ACF was used to cancel random surface “noise” and identify any spatial periodicity via repetitive ACF peaks or spatially correlated noise. Periodicity at shorter spatial wavelengths was observed for no doping and low doping levels, while smaller correlations were observed for relatively higher boron concentration. These semiquantitative spatial analyses may prove useful in comparing synthesis techniques and varying compositional makeups of diamond films and other technologically important electronic materials. These findings in terms of critical exponents are also correlated with traditional Raman spectroscopy and x-ray diffraction structural properties, thus helping to provide insight into the growth kinetics, albeit in reverse manner.     

Autocorrelation function and power spectral density of complexphase modulated signals derived from full response CPM

A class of digital phase-modulated signals called DCPM (digital complex phase-modulated) signals is introduced. In this class, the imaginary part of the phase is obtained from the real part by a linear time-invariant transformation. A method for computing the autocorrelation function (ACF) of DCPM is presented. It is shown that the ACF does not always exist. The power spectral density of DCPM is computed for Hilbert, identity, and zero transforms. It is also shown that DCPM with the Hilbert transform has a suppressed sideband and can yield significant bandwidth savings over zero transform schemes     

基于GPU通用计算平台的乐谱自动识别系统设计

在GPU通用计算平台上实现了一个钢琴独奏乐曲的乐谱识别系统,它读取WAV格式音频文件,利用GPU通用计算技术加速自相关函数算法来实现音高的识别,并综合考虑短时能量和基音周期的变化进行节拍划分。通过实际测试,验证了该乐谱识别系统的准确性,并证明了GPU并行计算对系统计算效率提升的效果：将计算时间减少到传统CPU计算时间的16%左右。     

Infinite series representations of the trivariate and quadrivariate nakagami-m distributions

In this paper, using Miller's approach and Dougall's identity, we derive new infinite series representations for the quadrivariate Nakagami-m joint density function, cumulative distribution function (cdf) and characteristic functions (chf). The classical joint density function of exponentially correlated Nakagami-m variables can be identified as a special case of the joint density function obtained here. Our results are based on the most general arbitrary correlation matrix possible. Moreover, the trivariate density function, cdf and chf for an arbitrary correlation matrix are also derived from our main result. Bounds on the series truncation error are also presented. Finally, we develop several representative applications: the outage probability of triple branch selection combining (SC), the moments of the equal gain combining (EGC) output signal to noise ratio (SNR) and the moment generation function of the generalized SC(2,3) output SNR in an arbitrarily correlated Nakagami-m environment. Simulation results are also presented to verify the accuracy of our theoretical results.     

Statistical analysis of azimuth streaks observed in digitallyprocessed CASSIE imagery of the sea surface

During the Canberra synthetic-aperture radar sea imaging experiment in 1987 (CASSIE 87), numerous azimuth streaks were observed by the X-band SAR. The authors analyzed the first- and second-order statistical properties of the CASSIE data, containing the images of the sea surface where wave breaking is considered to be present. The probability density function (PDF) and higher order intensity moments are first analyzed for image areas containing few and many streaks. The theoretical PDFs that fit the measured PDFs are identified. The two-dimensional intensity autocorrelation functions (ACFs) of images processed at different processor focal settings are computed and discussed to identify the predominant scatterers' motions. From these experimental results, a scattering model is postulated to account for the non-Rayleigh distribution and correlation of scattering amplitude, and the motion of scatterers. Using the model, the ACF of the range radar cross section is estimated from the image ACF and attempts are made to predict the azimuth component of the image ACF and the scene coherence time     

间歇混沌合成1/f噪声的相关特性分析

本文利用非线性随机微分方程来合成间歇混沌信号,针对该信号表现出的1/f噪声特征,在不同消失矩的小波基下进行相关特性分析.仿真结果发现,在功率谱的中间频段内,该信号的功率谱密度表现出典型的1/f噪声特性,其小波变换系数方差与相应的小波尺度呈对数线性关系;且在该频段内,部分尺度下该间歇性信号的小波变换系数的相关性随小波基的消失矩的增大而减小,在另一部分尺度下该相关性则随着消失矩的增大而增大.实验结果表明,随小波消失矩的增大,并非在所有尺度下小波变换对该间歇性信号均具有去相关作用.论文讨论了小波变换系数的方差和尺度的关系,详细分析了小波变换系数的相关性随小波消失矩的变化趋势.     

On the application of the GTD-MM technique and its limitations

In 1975 two techniques were published that combined the method of moments (MM) and the geometrical theory of diffraction (GTD). One technique extended the moment method through the use of the GTD while the second used the moment method to solve for unknown diffraction coefficients, thereby extending the use of the GTD. It is the latter method that is considered in this paper and is referred to as the GTD-MM technique. One problem area that existed with the original GTD-MM work was associated with a field incident along or nearly along one wall of a wedge structure. An improved series representation for the diffracted current that is sufficient at all incidence angles is shown. The improved formulation is then applied to the problem of bistatic scattering by a three-sided pyramid. Radar cross section (RCS) results that compare very well with experimental measurements are obtained. This is believed to be the first use of the GTD-MM technique in treating a three-dimensional geometry.     

非线性散射介质内辐射传递的积分矩方法

提出了求解非线性散射介质内辐射传递的积分矩方法.将辐射传递方程中散射相函数的积分项转化为辐射强度各阶矩的线性组合.散射相函数为勒让德多项式展开形式,辐射强度矩的最高阶数与散射相函数的展开项数相同.将原本复杂的积分微分方程转化为微分方程,通过积分法求解此方程.积分矩方法不需要对立体角进行离散,不会引起射线效应.积分矩方法...     

Computing Timing Jitter From Phase Noise Spectra for Oscillators and Phase-Locked Loops With White and$1/f$Noise

Phase noise and timing jitter in oscillators and phase-locked loops (PLLs) are of major concern in wireless and optical communications. In this paper, a unified analysis of the relationships between time-domain jitter and various spectral characterizations of phase noise is first presented. Several notions of phase noise spectra are considered, in particular, the power-spectral density (PSD) of the excess phase noise, the PSD of the signal generated by a noisy oscillator/PLL, and the so-called single-sideband (SSB) phase noise spectrum. We investigate the origins of these phase noise spectra and discuss their mathematical soundness. A simple equation relating the variance of timing jitter to the phase noise spectrum is derived and its mathematical validity is analyzed. Then, practical results on computing jitter from spectral phase noise characteristics for oscillators and PLLs with both white (thermal, shot) and$bf 1/f$noise are presented. We are able to obtain analytical timing jitter results for free-running oscillators and first-order PLLs. A numerical procedure is used for higher order PLLs. The phase noise spectrum needed for computing jitter may be obtained from analytical phase noise models, oscillator or PLL noise analysis in a circuit simulator, or from actual measurements.     

Electromagnetic response of two crossing, infinitely long, thinwires

The electromagnetic coupling of two crossed thin wires of infinite length is considered. Two coupled integral equations are obtained, given in terms of generalized impedance functions, for the spectral currents flowing in each wire. The wires may be in a homogeneous medium or over a half-space. The numerical implementation focuses, however, only on the former. The numerical solution may be obtained by either applying moment or multiple scattering methods. The solution obtained from the method of moments is applicable for any wire spacing. Obversely, the multiple scattering method leads to a convenient matrix series solution, which shows that the coupling between wires is proportional to 1/d ² (where d is the wire separation) plus higher order scattering terms     

Computation of fields in an arbitrary shaped heterogeneousdielectric or biological body by an iterative conjugate gradient method

Electromagnetic (EM) fields in a three-dimensional, arbitrarily shaped, heterogeneous dielectric or biological body illuminated by a plane wave are computed by an iterative conjugate gradient method. The method is a generalized method of moments applied to the volume integral equation. Because no matrix is explicitly involved or stored, the method is capable of computing EM fields in objects an order of magnitude larger than those that can be handled by the conventional method of moments. Excellent numerical convergence is achieved. Perfect convergence to the result of the conventional moment method using the same basis and weighted with delta functions is consistently achieved in all the cases computed, indicating that these two algorithms (direct and iterative) are equivalent     

Estimating the Effective Sample Size to Select Independent Measurements in a Reverberation Chamber

In reverberation chambers (RCs), measurements are usually performed by changing the boundary conditions using a mode stirrer. The major difficulty is to select uncorrelated samples in order to make a statistical analysis of the data. Furthermore, the knowledge of the number of independent samples is of crucial importance to assess the measurement accuracy. To evaluate whether measured data are independent, the conventional method compares the autocorrelation function (ACF) with the critical value 0.37. However, this criterion is generally not appropriate because the ACF probability density function (pdf) depends strongly on the sample size. For a measurement series of length N, the effective sample size (ESS) is defined as the number N' < N of independent samples, which would provide the same information as the N-size sample. This paper aims to provide a new method based on autoregressive (AR) models and the central limit theorem (CLT) in the case of dependent data, for estimating the ESS. The proposed method is easy to implement since it requires only the knowledge of simple statistical parameters. Moreover, it provides useful guidelines to assess the maximum number of independent samples available with the mode stirrer. Experimental results are in good agreement with the theoretical models, either for the electric field or the received power.     

Target recognition in SAR images using radial Chebyshev moments

In this study, a new algorithm for classification of ground vehicles from standard synthetic aperture radar (SAR) images is proposed. Radial Chebyshev moment (RCM) is a discrete orthogonal moment that has distinctive advantages over other moments for feature extraction. Unlike invariant moments, its orthogonal basis leads to having minimum information redundancy, and its discrete characteristics explore some benefits over Zernike moments (ZM) due to having no numerical errors and no computational complexity owing to normalization. In this context, we propose to use RCM as the feature extraction mechanism on the segmented image and to compare results of the fused images with both Zernike and radial Chebyshev moments. Firstly, by applying different threshold target and shadow parts of each SAR images are extracted separately. Then, segmented images are fused based on the combination of the extracted segmented region, segmented boundary and segmented texture. Experimental results will verify that accuracy of RCM, which improves significantly over the ZM. Ten percent improvement in the accuracy is obtained by using RCM and fusion of segmented target and shadow parts. Furthermore, feature fusion improves the total accuracy of the classification as high as 6%.     

Quadratic system identification using higher order spectra ofi.i.d. signals

The properties of higher order moment sequences and higher order spectral moments of an i.i.d. (independent, identically distributed) process up to fourth-order are discussed. These properties are utilized to develop algorithms to identify time-invariant nonlinear systems, which can be represented by second-order Volterra series and which are subjected to an i.i.d. input. A relatively simple solution for estimating the linear and quadratic transfer functions, which requires neither the calculation of the higher order spectral moments of the input for various frequencies nor the calculation of the inverse of matrix, is shown to exist, even though the second-order Volterra series is not an orthogonal model for an i.i.d. input (unless the input is a white Gaussian process)