Spectral analysis of non-linear systems involving square-law operations

This paper contains a number of useful theoretical formulas to analyze the frequency domain properties of Gaussian input data passing through non-linear square-law systems. Special bispectral density functions are defined and applied that are functions of a single variable. From measurements of input data and output data only, results are obtained to identify the separate frequency response functions for two models of linear systems in parallel with non-linear square-law systems. Non-linear coherence functions are defined from these models which determine the proportion of the output spectrum due to the non-linear operations. Together with ordinary coherence functions, a measured output spectrum for these models can be decomposed into three components representing the linear operations, the non-linear operations, and the remaining uncorrelated noise effects. This material indicates also how to analyze other types of non-linear models by employing similar techniques.     

Estimation of the impulse response of ultra-wide-band systems

The time and frequency algorithms of impulse response recovery in linear ultra-wide-band systems by a finite set of digital data presenting the input and output signals are proposed. The results of approbation of these algorithms by numerical simulation in the presence of additive Gaussian noise in the output signal are given. It is shown that the systems with noise-like signals at the input have the largest noise immunity in the estimation of impulse response. Institute for High-Current Electronics of the Russian Academy of Sciences, Tomsk, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 41, No. 9, pp. 1195–1206, September, 1998.     

Identification of modal parameters including unmeasured forces and transient effects

In this paper, a frequency-domain method to estimate modal parameters from short data records with known input (measured) forces and unknown input forces is presented. The method can be used for an experimental modal analysis, an operational modal analysis (output-only data) and the combination of both. A traditional experimental and operational modal analysis in the frequency domain starts respectively, from frequency response functions and spectral density functions. To estimate these functions accurately sufficient data have to be available. The technique developed in this paper estimates the modal parameters directly from the Fourier spectra of the outputs and the known input. Instead of using Hanning windows on these short data records the transient effects are estimated simultaneously with the modal parameters. The method is illustrated, tested and validated by Monte Carlo simulations and experiments. The presented method to process short data sequences leads to unbiased estimates with a small variance in comparison to the more traditional approaches.     

FREQUENCY DOMAIN ARX MODEL AND MULTI-HARMONIC FRF ESTIMATORS FOR NON-LINEAR DYNAMIC SYSTEMS

Non-linear dynamic systems respond at frequencies other than the excitation frequency; however, standard frequency response function estimators for linear systems do not accommodate this harmonic distortion. A new multi-harmonic frequency response function estimator that utilizes discrete frequency models for non-linear systems is introduced here. The multi-harmonic estimator relates the frequency response at each frequency to the input and output spectra within a given frequency band in the same way that autoregressive exogenous input models relate inputs and outputs at particular samples in the time domain. Overdetermined, least-mean-squares calculations are used to minimize model error throughout a frequency band rather than at a single frequency as in the corresponding linear estimators. The resulting multi-harmonic frequency response function models are non-parametric (e.g., vary with amplitude) when linear functions are used and parametric when non-linear functions are used. A new sensitive indicator for experimentally characterizing non-linearity is introduced.     

外腔共振和频系统中阻抗匹配的理论研究

外腔共振是提高和频效率的有效方法. 实现外腔共振高效和频需要基频光高效地耦合到外部谐振腔中, 因此系统要达到阻抗匹配. 本文分别建立了双波长和单波长外腔共振和频系统的理论模型, 分析了腔增强因子与耦合腔镜反射率、入射基频光功率等参数的依赖关系, 通过数值模拟获得最优化的共振光耦合腔镜反射率, 使系统达到阻抗匹配, 提高和频效率. 研究表明, 无论双波长还是单波长外腔共振和频系统, 共振基频光的最佳耦合腔镜反射率只会随着另一束共振或者不共振的基频光入射功率的增加而减小, 而其本身的入射功率变化则影响较小; 进一步分析表明, 若共振基频光的耦合腔镜反射率超过阻抗匹配值, 和频光功率将会迅速减小, 而小于阻抗匹配值时, 和频光功率减少速度相对较慢, 因此实验过程中要尽量避免过耦合的情况出现. 本文的理论分析过程将对外腔和频实验有一定的指导意义.     

环形谐振腔频率响应特性研究

分析了方形环形谐振腔对S线偏光和P线偏光的频率响应特性,发现输入两个频率间隔相差很小的S线偏光和P线偏光都能引起环形谐振腔的谐振,其中S线偏光谐振峰频率特性更适于环形谐振腔的稳频。通过搭建环形谐振腔频率响应特性测试系统,从实验上验证了理论计算的正确性。对于环形谐振腔的稳频和调腔具有参考意义。     

Nonlinear identification of NMR spin systems by adaptive filtering

In this paper, we present two new methods for identifying NMR spin systems. These methods are based on nonlinear adaptive filtering. The spin system is assumed to be time-invariant with memory. The first method uses a truncated discrete Volterra series to describe the nonlinear relationship between excitation (input) and system response (output). First-, second-, and third-order kernels of this series are estimated employing the least mean square (LMS) algorithm. Three parallel filters can then model the NMR spin system so that its output is no more than simple sum of three convolution products between combinations of the input signal and filters coefficients. It is also shown that the contribution of the Volterra second-order term to the total system response is neglected compared with the contributions of the first- and the third-order terms. In the second identification method, the output signal is related to the input signal through a recursive nonlinear difference equation with constant coefficients. The LMS algorithm is used again to estimate the equation coefficients. The two methods are validated with a simulated NMR system model based on Bloch equations. The results and the performances of these methods are analyzed and compared. It is shown that our methods permit a simple identification of NMR spin systems. The field of applications of this study is promising in the optimization of NMR signal detection, especially in the cases of low signal-to-noise ratios where optimum signal filtering and analysis must be performed.     

The effects of nonlinearity on the output frequency response of a passive engine mount

In this paper, the new concept of output frequency-response function (OFRF) that was derived recently by the authors from the Volterra-series theory of nonlinear systems is briefly introduced. An effective algorithm is proposed to determine the monomials in the OFRF-based representation of the output frequency response of nonlinear systems. The results are then used to analyze the output frequency response of a passive engine mount. Important conclusions regarding the effects of system nonlinearity on the output frequency-response behaviors of the engine mount are reached via theoretical analysis and verified by simulation studies. These conclusions are of significant importance for the analysis and design of vibration isolators such as engine mounts in practice.     

Neural network models of sound localization based on directional filtering by the pinna.

Three-layer neural-network functions were developed to transform spectral representations of pinna-filtered stimuli at the input to a space-mapped representation of sound-source direction at the output. The inputs are modeled after transfer functions of the external ear of the cat; the output is modeled on the spatial sensitivity of superior colliculus neurons. Network solutions are obtained by backpropagation and by a method that enforces uniform task distribution in the hidden layer of the model. Solutions are characterized using bandlimited inputs to study the relative strength of potential sound localization cues in various frequency regions. This analysis suggests that the frequency region containing the first spectral notch (5-18 kHz) provides the best localization cues. Response properties of model neurons were studied using input patterns modeled after auditory nerve response profiles to pure tones at various frequencies and sound levels. The response properties of hidden layer model neurons resemble cochlear nucleus types III and IV and their composites. Neurons in both hidden and output layers show the properties of spectral notch detectors. Although neural networks have limitations as models of real neural systems, the results illustrate how they can provide insight into the computation of complex transformations in the nervous system.     

The effects of window delay, delinearization, and frequency on tone-burst otoacoustic emission input/output measurements

Tone-burst otoacoustic emissions (TBOAEs) are a potential tool for objectively examining cochlear activity in humans. However, their use requires knowledge of how the TBOAE input/output depends on measurement and analysis paradigms. The present experiment examined the effect of variations in response-window timing, response delinearization, and local changes in stimulus frequency on TBOAE input/output measurement. None of these experimental manipulations had a profound effect on TBOAE measurements as long as reasonable parameter choices were made. Nonetheless, judicial choice of the experimental parameters can optimize the assessment of BM I/O functions. It is concluded that the consistency of TBOAE I/O across the parameters tested makes it a viable tool to consider for examining human cochlear activity.     

Approximate and Exact Small Signal Analysis for Single-Mode Fiber Near Zero Dispersion Wavelength with Higher Order Dispersion

This article presents the comparison of approximate and exact small-signal theories for analyzing the influence of the higher-order dispersion terms on dispersive optical communication systems operating near zero dispersion wavelength for linear single-mode fiber. For the approximate theory, the generalized conversion matrix has been reported and gives the transfer function of intensity and phase from the fiber input to fiber output for a laser source including the influence of any higher-order dispersion term. In addition, expressions for the small-signal frequency response and the relative intensity noise (RIN) response of an ultrafast laser diode including noises are derived. However, it is observed that the approximation assumed for the second-order dispersion term for the approximate analysis is not valid. From the approximate theory, the exact generalized conversion matrix and exact expressions for small-signal frequency response and relative intensity noise (RIN) are obtained. We show that for the exact theory, the second-order dispersion term has no effect on intensity and frequency response even at large modulating frequencies and large propagation distances contrary to the approximate theory as reported by other authors. But we show that third-order dispersion term certainly has some minute impact on the frequency and RIN response for long distance links at high modulating frequencies.     

Approximate and Exact Small Signal Analysis for Single-Mode Fiber Near Zero Dispersion Wavelength with Higher Order Dispersion

This article presents the comparison of approximate and exact small-signal theories for analyzing the influence of the higher-order dispersion terms on dispersive optical communication systems operating near zero dispersion wavelength for linear single-mode fiber. For the approximate theory, the generalized conversion matrix has been reported and gives the transfer function of intensity and phase from the fiber input to fiber output for a laser source including the influence of any higher-order dispersion term. In addition, expressions for the small-signal frequency response and the relative intensity noise (RIN) response of an ultrafast laser diode including noises are derived. However, it is observed that the approximation assumed for the second-order dispersion term for the approximate analysis is not valid. From the approximate theory, the exact generalized conversion matrix and exact expressions for small-signal frequency response and relative intensity noise (RIN) are obtained. We show that for the exact theory, the second-order dispersion term has no effect on intensity and frequency response even at large modulating frequencies and large propagation distances contrary to the approximate theory as reported by other authors. But we show that third-order dispersion term certainly has some minute impact on the frequency and RIN response for long distance links at high modulating frequencies.     

Multiline output from a spin-flip laser

Multiplicity of the output frequency of a spin-flip laser, caused by the simultaneous multiline operation of the CO pump laser, is identified. This multiplicity is shown to arise from a four-wave mixing process for which only a single input threshold intensity exists for oscillation. Experimental data are presented together with a determination of the interdependence of the input and output frequency power ratio.     

Calculation of the frequency response in step-index plastic optical fibers using the time-dependent power flow equation

The time-dependent power flow equation, which is reduced to its time-independent counterpart is employed to calculate frequency response and bandwidth in addition to mode coupling and mode-dependent attenuation in a step-index plastic optical fiber. The frequency response is specified as a function of distance from the input fiber end. This is compared to reported measurements. Mode-dependent attenuation and mode dispersion and coupling are known to be strong in plastic optical fibers, leading to major implications for their frequency response in data transmission systems.     

Parametric time domain analysis of the multiple input/scalar output problem: The source identification problem

A multiple input/scalar output stationary time series identification problem is considered from a parametric model time domain point of view. Particular emphasis is on the source identification problem. Closed form formula estimates of the individual source power contributions are expressed in terms of sample correlations that are obtained from the observed input and output time series and from parametric models fitted to that data. The estimates of the noise power contributions are asymptotically jointly normally distributed. The mean values and covariance matrix of those estimates yield confidence interval estimates of the individual and joint power contributions.The motivation for developing a rational polynomial transfer function or ARMA model of the multi-input scalar output plus additive noise situation is given. A two correlated input/single output version of this model is considered for a Monte Carlo simulation study. Parametric ARMA and approximate AR models are fitted to the simulated data. The asymptotic normality, and the distribution of the mean and covariances of the source power contribution computed from the ARMA and AR models are appraised.Several facets of the relative performance of windowed periodogram and AR model spectral analysis are examined for the multiple input/scalar output identification problem. The points that are emphasized are that conventional windowed periodogram spectral analysis is subjective, not particularly satisfactory for the sharp spectral peak situation that is commonly encountered in vibration data analysis and very likely not as good as “objective” Akaike criterion order AR modelled spectral analysis.     

An efficient Schottky-varactor frequency multiplier at millimeter waves. Part III. Quadrupler

In this research the efficiency of a millimeter-wave Schottky-varactor quadrupler was studied. Theoretical simulations were carried out by using a nonlinear analysis program to find the optimum embedding impedances for a given diode. Emphasis was placed on the study of optimum idlers at the 2nd and 3rd harmonics, which are essential for a high quadrupling efficiency. For experimental verification a quadrupler for 140–155 GHz output frequency range with fixed idler terminations was constructed. This quadrupler was tested with different output configurations. A 10% tunable bandwidth was obtained with output power in the range of 1.5–2.7 mW whenP _in =40 mW. The highest efficiency measured was 11.3% at 148 GHz with 10 mW input power.     

Solutions for the multiple input/output poblem

This paper provides new solutions for the general multiple input/output problem involving arbitrary stationary random processes by using a special representation for random records. Mathematical results are obtained here for partial coherence functions, multiple coherence functions, decomposition of output spectra into physically meaningful components, and other useful quantities. These results are relatively simple to understand and to compute compared to previously known least-squares methods. Engineering applications and error analysis matters are also considered.     

Frequency domain analysis and identification of block-oriented nonlinear systems

Block-oriented nonlinear models including Wiener models, Hammerstein models and Wiener-Hammerstein models, etc. have been extensively applied in practice for system identification, signal processing and control. In this study, analytical frequency response functions including generalized frequency response functions (GFRFs) and nonlinear output spectrum of block-oriented nonlinear systems are developed, which can demonstrate clearly the relationship between frequency response functions and model parameters, and also the dependence of frequency response functions on the linear part of the model. The nonlinear part of these models can be a more general multivariate polynomial function. These fundamental results provide a significant insight into the analysis and design of block-oriented nonlinear systems. Effective algorithms are therefore proposed for the estimation of nonlinear output spectrum and for parametric or nonparametric identification of nonlinear systems. Compared with some existing frequency domain identification methods, the new estimation algorithms do not necessarily require model structure information, not need the invertibility of the nonlinearity and not restrict to harmonic inputs. Simulation examples are given to illustrate these new results.     

气流扬声器振动系统的设计原理

本文用等效电路方法分析了电动气流扬声器振动系统的特性,求得了气流扬声器的输入阻抗和位移振幅的频率特性,并把结果用于典型扬声器,说明用等效电路分析指导气流扬声器设计的作用。气流扬声器振动系统所需的电功率与其机械共振频率的四次方成正比,其声辐射主要限于共振频率以下,因而高频特性较差。求得了在共振频率以下,频率响应平直的最佳条件,实验表明,在最佳条件下,气流扬声器的高频特性随着磁隙中的磁感应强度的增加仍稍有提高。实验结果符合理论分析,测得气流扬声器喇叭喉部的声压级在不同情况下达181分贝或184.8分贝(零分贝等于2×10^-5牛顿/米²)。     

A computational algorithm for computing nonlinear auditory frequency selectivity.

Computational algorithms that mimic the response of the basilar membrane must be capable of reproducing a range of complex features that are characteristic of the animal observations. These include complex input output functions that are nonlinear near the site's best frequency, but linear elsewhere. This nonlinearity is critical when using the output of the algorithm as the input to models of inner hair cell function and subsequent auditory-nerve models of low- and high-spontaneous rate fibers. We present an algorithm that uses two processing units operating in parallel: one linear and the other compressively nonlinear. The output from the algorithm is the sum of the outputs of the linear and nonlinear processing units. Input to the algorithm is stapes motion and output represents basilar membrane motion. The algorithm is evaluated against published chinchilla and guinea pig observations of basilar membrane and Reissner's membrane motion made using laser velocimetry. The algorithm simulates both quantitatively and qualitatively, differences in input/output functions among three different sites along the cochlear partition. It also simulates quantitatively and qualitatively a range of phenomena including isovelocity functions, phase response, two-tone suppression, impulse response, and distortion products. The algorithm is potentially suitable for development as a bank of filters, for use in more comprehensive models of the peripheral auditory system.