NMR spectral quantitation by principal component analysis. III. A generalized procedure for determination of lineshape variations

We present a general procedure for automatic quantitation of a series of spectral peaks based on principal component analysis (PCA). PCA has been previously used for spectral quantitation of a single resonant peak of constant shape but variable amplitude. Here we extend this procedure to estimate all of the peak parameters: amplitude, position (frequency), phase and linewidth. The procedure consists of a series of iterative steps in which the estimates of position and phase from one stage of iteration are used to correct the spectra prior to the next stage. The process is convergent to a stable result, typically in less than 5 iterations. If desired, remaining linewidth variations can then be corrected. Correction of (typically) unwanted variations of these types is important not only for direct peak quantitation, but also as a preprocessing step for spectral data prior to application of pattern recognition/classification techniques. The procedure is demonstrated on simulated data and on a set of 992 (31)P NMR in vivo spectra taken from a kinetic study of rat muscle energetics. The proposed procedure is robust, makes very limited assumptions about the lineshape, and performs well with data of low signal-to-noise ratio.     

Spectral analysis of a nonlinear oscillator driven by random and periodic forces. I. Linearized theory

We have combined the techniques of statistical and harmonic linearization to develop a linearized approximation theory for the calculation of the second-order statistics (i.e., autocorrelation functions and spectral densities) of nonlinear systems driven by both random and periodic forces. For the special case of a Duffing oscillator (a damped anharmonic oscillator with a cubic nonlinearity) driven by Gaussian white noise and by a sinusoidal force, explicit expressions for the renormalized (linearized) frequency, the autocorrelation function, and the spectral density of the oscillator displacement in terms of all the system parameters have been derived. We have determined the region of the parameter space in which the applied periodic force has a significant influence on the second-order statistics of the oscillator.This research was supported by the Office of Naval Research, by the National Science Foundation under grant No. CHE78-21460 and by a grant from Charles and Reneé Taubman.     

A statistical analysis of NMR spectrometer noise

Estimation of NMR spectral parameters, using e.g. maximum likelihood methods, is commonly based on the assumption of white complex Gaussian noise in the signal obtained by quadrature detection. Here we present a statistical analysis with the purpose of discussing and testing the validity of this fundamental assumption. Theoretical expressions are derived for the correlation structure of the noise under various conditions, showing that in general the noise in the sampled signal is not strictly white, even if the thermal noise in the receiver steps prior to digitisation can be characterised as white Gaussian noise. It is shown that the noise correlation properties depend on the ratio between the sampling frequency and the filter cut-off frequency, as well as the filter characteristics. The theoretical analysis identifies conditions that are expected to yield non-white noise in the sampled signal. Extensive statistical characterisation of experimental noise confirms the theoretical predictions. The statistical methods outlined here are also useful for residual analysis in connection with validation of the model and the parameter estimates.     

噪声间关联对原子激光谱密度的影响

在描述原子激光强度的速率方程中，考虑了量子噪声和热噪声、以及它们的关联以后，计算了原子激光的关联函数和功率谱密度。发现不仅噪声对原子激光的统计性质有影响，而且，噪声间的关联会使得原子激光的谱密度发生从单峰到双峰、或三峰的相变。这种相变可以用凝聚体干涉条纹间距的变化来观察。进一步又讨论了噪声的关联时间对原子激光谱密度的影响。     

A critique on the application of infrared photodetector theory

The physical and mathematical framework underlying photodetector theory is appraised, with particular interest in those aspects relevant to practical device application. The mathematical assumptions and conventions on which signal and r.m.s. noise calculations are based are examined, together with the relationships between the characteristic parameters, responsivity and detectivity, and device spectral response, frequency response and linearity. An equivalent ramp-function spectral response based on the definition of an effective cutoff wavelength is derived and is shown to be useful for cases where device data are incomplete. The standard expressions for responsivity, detectivity, signal and noise currents, signal-to-noise ratio and noise-equivalent temperature difference are examined with particular interest in their application to device use and IR system design.     

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.     

Bayesian Deconvolution

Bayesian probability has been applied to the problem of estimating the true spectral lineshape from an experimental peak with prior knowledge of the instrumental contribution. The results demonstrate that Bayesian deconvolution provides excellent estimates of the parameters defining the true spectral lineshape even from strongly overlapping or broadened peaks in the presence of significant noise levels.     

The noise reduction of flanking paths

A series of simple expressions are derived which enable flanking transmission to be calculated for most common situations. The parameters that affect flanking transmission are described, and design data necessary for the calculation of flanking path noise reduction is given. Usually, each flanking path will be less important than the direct path but, since there are many such paths, flanking will often be important in the overall transmission of sound between two rooms.     

A median-Gaussian filtering framework for Moiré pattern noise removal from X-ray microscopy image

Moiré pattern noise in Scanning Transmission X-ray Microscopy (STXM) imaging introduces significant errors in qualitative and quantitative image analysis. Due to the complex origin of the noise, it is difficult to avoid Moiré pattern noise during the image data acquisition stage. In this paper, we introduce a post-processing method for filtering Moiré pattern noise from STXM images. This method includes a semi-automatic detection of the spectral peaks in the Fourier amplitude spectrum by using a local median filter, and elimination of the spectral noise peaks using a Gaussian notch filter. The proposed median-Gaussian filtering framework shows good results for STXM images with the size of power of two, if such parameters as threshold, sizes of the median and Gaussian filters, and size of the low frequency window, have been properly selected.     

Generalized Stokes parameters of random electromagnetic vortex beams propagating through atmospheric turbulence

By using the extended Huygens–Fresnel principle, the analytical expressions for the generalized Stokes parameters of random electromagnetic Gaussian Schell-model (GSM) vortex beams propagating through atmospheric turbulence are derived, and used to study the changes in spectral Stokes parameters of random electromagnetic GSM vortex beams in atmospheric turbulence and to compare the results of random electromagnetic GSM vortex-free beams. The influence of atmospheric turbulence on the spectral Stokes parameters is analyzed. The validity of our results is interpreted physically.     

光谱信号的小波去噪新技术

光谱分析中,噪声的存在常影响分析的准确度和检测限。现有滤波方法在光谱信号除噪方面有种种缺陷。文章充分利用小波在信号处理方面的优良特性,提出了Mexican Hat小波滤波算法,它选用Mexican Hat小波函数构造滤波项,利用滤波项与原始信号作用,从而实现信号与噪音的分离。该方法无论对低频或高频信号均适用,除噪完全,即使对信噪比为1的高噪声信号也能获取满意的处理结果。运用这一技术处理光谱信号,简单快速、结果可靠,处理后峰位置、峰高、峰面积误差分别小于0.2%,3.2%,1.1%。大量实验表明,本方法能有效提高光谱分析的准确度。     

Determination of the amplitude and the phase of the elements of electric cross-spectral density matrix by spectral measurements

The amplitudes and the phases of the elements of electric cross-spectral density matrix are determined experimentally for a pair of points in the cross-section of an expanded laser beam. A modified version of the Young’s interferometer is used as an experimental tool, which separates the beams emerging from the double-slit widely and provides ease in insertion of polarizers and half wave rotators in individual beams. To determine these complex elements of the cross-spectral density matrix, the experimentally obtained values of the spectral densities at an off-axis point are put in the mathematical expressions derived by us using the spectral interference law. The four complex generalized Stokes parameters are also determined using the linear combinations of the matrix elements. This unique but simple experimental approach for determining both the two-point parameters might provide a means to investigate the polarization and the coherence properties of the random electromagnetic beams on propagation.     

Temporal changes in a complex spectral profile

The spectral properties of a complex stimulus (rippled noise) were varied over time, and listeners were asked to discriminate between this stimulus and a flat-spectrum, stationary noise. The spacing between the spectral peaks of rippled noise was changed sinusoidally as a function of time, or the location of the spectral peaks of rippled noise was moved up and down the spectrum as a sinusoidal function of time. In most conditions, listeners were able to make the discriminations up to rates of temporal modulation of 5-10 cycles per second. Beyond 5-10 cps the rippled noise with the temporally varying peaks was indiscriminable from a flat (nonrippled) noise. The results suggest that for temporal changes in the spectral peaks of rippled noise, listeners cannot monitor the output of a single (or small number of) auditory channel(s) (critical bands), or that the mechanism used to extract the perceptual information from these stimuli is slow. Temporal variations in the spectral properties of rippled noise may relate to temporal changes in the repetition pitch of complex sounds, the temporal properties of the coloration added to sound in a reverberant environment, and the nature of spectral peak changes such as those that occur in speech-formant transitions. The results are relevant to the general issue of the auditory system's ability to extract information from a complex spectral profile.     

Effect of inertial mass on a linear system driven by dichotomous noise and a periodic signal

A linear system driven by dichotomous noise and a periodic signal is investigated in the underdamped case. The exact expressions of output signal amplitude and signal-to-noise ratio (SNR) of the system are derived. By means of numerical calculation, the results indicate that (i) at some fixed noise intensities, the output signal amplitude with inertial mass exhibits the structure of a single peak and single valley, or even two peaks if the dichotomous noise is asymmetric; (ii) in the case of asymmetric dichotomous noise, the inertial mass can cause non-monotonic behaviour of the output signal amplitude with respect to noise intensity; (iii) the curve of SNR versus inertial mass displays a maximum in the case of asymmetric dichotomous noise, i.e., a resonance-like phenomenon, while it decreases monotonically in the case of symmetric dichotomous noise; (iv) if the noise is symmetric, the inertial mass can induce stochastic resonance in the system.     

具有时滞状态反馈的随机Van der Pol系统的动力学研究

研究了时滞及时滞反馈控制参数对Van der Pol系统极限环幅值的影响. 运用自适应的平均场近似方法给出了系统的线性化近似及系统参数Lyapunov稳定性的边界条件, 同时给出了Van der Pol系统的关联时间和功率谱密度的数值模拟结果. 通过与平均场近似下的解析结果比较后发现, 数值模拟结果和理论结果符合.进一步讨论了时滞反馈控制参数、噪声强度以及时滞对关联时间和功率谱密度的影响. 关键词： 平均场近似 关联时间 Lyapunov稳定性     

5- and 6-pulse electron spin echo envelope modulation (ESEEM) of multi-nuclear spin systems

In 3-pulse ESEEM and the original 4-pulse HYSCORE, nuclei with large modulation depth (k approximately 1) suppress spectral peaks from nuclei with weak modulations (k approximately 0). This cross suppression can impede the detection of the latter nuclei, which are often the ones of interest. We show that two extended pulse sequences, 5-pulse ESEEM and 6-pulse HYSCORE, can be used as experimental alternatives that suffer less strongly from the cross suppression and allow to recover signals of k approximately 0 nuclei in the presence of k approximately 1 nuclei. In the extended sequences, modulations from k approximately 0 nuclei are strongly enhanced. In addition, multi-quantum transitions are absent which simplifies the spectra. General analytical expressions for the modulation signals in these sequences are derived and discussed. Numerical simulations and experimental spectra that demonstrate the higher sensitivity of the extended pulse sequences are presented.     

Modelling and characterization of electrostatic current noise induced mechanically in wired wearable applications

By means of statistical modelling and measurement, the triboelectric current noise spectral density is evaluated for shielded cables in body-borne wired network subjected to mechanical stresses. Assuming a shot noise model, an expression for the current spectral density of the noise is derived. The efficiency of the methodology is demonstrated by measuring the triboelectric current noise in two shielded cables subjected to bending. Thereafter the parameters of the noise pulses' waiting time and amplitude probability density functions are extracted from measurement, thus enabling the computation of the current spectral density of the noise induced mechanically in body-borne wired networks.     

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.     

Quantum interference spectra at the difference-frequency generation in four-level atomic systems

Analytical expressions of the spectral functions have been derived for a number of induced excitations that occur near the difference-frequency generation in a four-level atomic system interacting with three laser fields. The spectral heights and subnatural line widths of the induced peaks depend on the intensities of the laser fields involved. The maximum heights of the induced peaks take positive, zero and negative values, indicating that the processes of absorption (attenuation), dark resonance and stimulated emission (amplification) are likely to occur near the difference-frequency generation, respectively. Received: 15 March 2002 / Revised version: 17 June 2002 / Published online: 8 January 2003 RID="*" ID="*"Corresponding author. Fax: +1-613-954-5242     

Fluctuations in doubly scattered laser light

Fluctuations in laser light, doubly scattered by brownian particles, were analysed by measuring the spectral noise power of the photodetector current. Scattering took place at two spatially separated systems of spherical particles. Analytic expressions for the field and intensity correlations are derived. The analytic expressions for the spectrum of the intensity fluctuations of the doubly scattered laser light demonstrate that the frequency dependence of the spectrum depends strongly of the geometry of the experimental arrangement. This is not the case for singly scattered light where in good approximation the spatial and temporal correlations can be separated analytically.Our measurements show that the noise spectrum of the doubly scattered radiation may have the same frequency dependence as the spectrum of the singly scattered light. However, there are conditions where the frequency dependence of the noise of the doubly scattered light diverges markedly from that of the singly scattered light.