Nonparametric identification of Hammerstein systems

A discrete-time nonlinear Hammerstein system is identified, and the correlation and frequency-domain methods for identification of its linear subsystem are presented. The main results concern the estimation of the nonlinear memoryless subsystem. No conditions concerning the functional form of the transform characteristic of the subsystem are made, and an algorithm for estimation of the characteristic is given. The algorithm is simply a nonparametric kernel estimate of the regression function calculated from dependent data. It is shown that the algorithm converges to the characteristic of the subsystem regardless of the probability distribution of the input variable. Pointwise as well as global consistencies are established. For Lipschitz characteristics the rate of the convergence in probability is O(n^-1/3 )     

Nonparametric identification of Wiener systems

A Wiener system, i.e., a system in which a linear dynamic part is followed by a nonlinear and memoryless one, is identified. No parametric restriction is imposed on the functional form of the nonlinear characteristic of the memoryless subsystem, and a nonparametric algorithm recovering the characteristic from input-output observations of the whole system is proposed. Its consistency is shown and the rate of convergence is given. An idea for identification of the impulse response of the linear subsystem is proposed. Results of numerical simulation are also presented     

Two-dimensional orthogonal wavelets with vanishing moments

We investigate a very general subset of 2-D, orthogonal, compactly supported wavelets. This subset includes all the wavelets with a corresponding wavelet (polyphase) matrix that can be factored as a product of factors of degree-1 in one variable. In this paper, we consider, in particular, wavelets with vanishing moments. The number of vanishing moments that can be achieved increases with the increase in the McMillan degrees of the wavelet matrix. We design wavelets with the maximal number of vanishing moments for given McMillan degrees by solving a set of nonlinear constraints on the free parameters defining the wavelet matrix and discuss their relation to regular, smooth wavelets. Design examples are given for two fundamental sampling schemes: the quincunx and the four-band separable sampling. The relation of the wavelets to the well-known 1-D Daubechies wavelets with vanishing moments is discussed     

Two-dimensional orthogonal filter banks and wavelets with linearphase

Two-dimensional (2-D) compactly supported, orthogonal wavelets and filter banks having linear phase are presented. Two cases are discussed: wavelets with two-fold symmetry (centrosymmetric) and wavelets with four-fold symmetry that are symmetric (or anti-symmetric) about the vertical and horizontal axes. We show that imposing the requirement of linear phase in the case of order-factorable wavelets imposes a simple constraint on each of its polynomial order-1 factors. We thus obtain a simple and complete method of constructing orthogonal order-factorable wavelets with linear phase. This method is exemplified by design in the case of four-band separable sampling. An interesting result that is similar to the one well-known in the one-dimensional (1-D) case is obtained: orthogonal order-factorable wavelets cannot be both continuous and have four-fold symmetry     

Analysis of stochastic gradient identification ofWiener-Hammerstein systems for nonlinearities with Hermite polynomialexpansions

This paper investigates the statistical behavior of a sequential adaptive gradient search algorithm for identifying an unknown Wiener-Hammerstein (1958) system (WHS) with Gaussian inputs. The WHS nonlinearity is assumed to be expandable in a series of orthogonal Hermite polynomials. The sequential procedure uses (1) a gradient search for the unknown coefficients of the Hermite polynomials, (2) an LMS adaptive filter to partially identify the input and output linear filters of the WHS, and (3) the higher order terms in the Hermite expansion to identify each of the linear filters. The third step requires the iterative solution of a set of coupled nonlinear equations in the linear filter coefficients. An alternative scheme is presented if the two filters are known a priori to be exponentially shaped. The mean behavior of the various gradient recursions are analyzed using small step-size approximations (slow learning) and yield very good agreement with Monte Carlo simulations. Several examples demonstrate that the scheme provides good estimates of the WHS parameters for the cases studied     

An orthogonal family of quincunx wavelets with continuously adjustable order.

We present a new family of two-dimensional and three-dimensional orthogonal wavelets which uses quincunx sampling. The orthogonal refinement filters have a simple analytical expression in the Fourier domain as a function of the order lamda, which may be noninteger. We can also prove that they yield wavelet bases of L2(R2) for any lambda > 0. The wavelets are fractional in the sense that the approximation error at a given scale a decays like O(a(lamda)); they also essentially behave like fractional derivative operators. To make our construction practical, we propose a fast Fourier transform-based implementation that turns out to be surprisingly fast. In fact, our method is almost as efficient as the standard Mallat algorithm for separable wavelets.     

Cancellation of nonlinearities in bandpass QAM systems

An orthogonalized input-output characterization of nonlinear bandpass quadrature amplitude modulation systems with memory is developed. The orthogonal expansion is used with a nonlinear canceller structure to counteract the effect of nonlinear distortion introduced by high-power amplifiers at the transmitter. It is shown through simulations that when the transmitted symbols are known at the canceller, relatively simple structures can eliminate the effect of the nonlinearity. Even when the transmitted symbols are not known at the canceller, the improvement in performance with the nonlinear canceller, with respect to a linear receiver, is significant     

Tolerance of nonlinearities in time-varying optimal systems

Nominally linear optimal-control regulating systems are examined with a view to assessing the amount of nonlinearity which can be tolerated in the input transducer. Using a suitable Lyapunov function, it is found that a large degree of nonlinearity will not disturb the stability of the system.     

Speed estimation in wireless systems using wavelets

A new technique is described for estimating the speed of a mobile station in a wireless system. The mobile speed maps the characteristic spatial scale of the received signal into a characteristic temporal scale. The continuous wavelet transform tracks changes in the temporal scale to estimate the mobile speed as a function of time. This technique requires neither knowledge of the average received power of the nonstationary signal nor adaptation of a temporal observation window, in contrast to other speed estimators given in the literature. Simulations show the tracking of a variable speed profile     

Dyadic-based factorizations for regular paraunitary filterbanks and M-band orthogonal wavelets with structural vanishing moments

Paraunitary filterbanks (PUFBs) can be designed and implemented using either degree-one or order-one dyadic-based factorization. This work discusses how regularity of a desired degree is structurally imposed on such factorizations for any number of channels M /spl ges/ 2, without necessarily constraining the phase responses. The regular linear-phase PUFBs become a special case under the proposed framework. We show that the regularity conditions are conveniently expressed in terms of recently reported M-channel lifting structures, which allow for fast, reversible, and possibly multiplierless implementations in addition to improved design efficiency, as suggested by numerical experience. M-band orthonormal wavelets with structural vanishing moments are obtained by iterating the resulting regular PUFBs on the lowpass channel. Design examples are presented and evaluated using a transform-based image coder, and they are found to outperform previously reported designs.     

Compensation for nonlinearities in third-generation mobile systems

A technique for compensating for nonlinear distortion in third-generation (3G) communication systems is presented. In these communication systems, the power-efficient amplification introduces both a widening of the transmitted pulse and nonlinear intersymbol interference. Novel structures are presented which are able to reduce simultaneously both unwanted effects. Examples are presented which show the performance of the compensators in typical digital channels     

Compactly supported orthogonal and biorthogonal square root 5-refinement wavelets with 4-fold symmetry

Recently, square root 5 -refinement hierarchical sampling has been studied and square root 5-refinement has been used for surface subdivision. Compared with other refinements, such as the dyadic or quincunx refinement, square root 5-refinement has a special property that the nodes in a refined lattice form groups of five nodes with these five nodes having different x and y coordinates. This special property has been shown to be very useful to represent adaptively and render complex and procedural geometry. When square root 5-refinement is used for multiresolution data processing, square root 5-refinement filter banks and wavelets are required. While the construction of 2-D nonseparable (bi)orthogonal wavelets with the dyadic or quincunx refinement has been studied by many researchers, the construction of (bi)orthogonal wavelets with square root 5-refinement has not been investigated. The main goal of this paper is to construct compactly supported orthogonal and biorthogonal wavelets with square root 5 -refinement. In this paper, we obtain block structures of orthogonal and biorthogonal square root 5-refinement FIR filter banks with 4-fold rotational symmetry. We construct compactly supported orthogonal and biorthogonal wavelets based on these block structures.     

Nonparametric recovery of multivariate functions with applications to system identification

The methodology for nonparametric fitting of multivariate functions is proposed. The mean-square error convergence and the strong convergence are proved.     

Nonparametric identification of discriminative information in bodysurface maps

A nonparametric method, based on the Kolmogorov-Smirnov (K-S) test was used to detect significant differences between classes of body surface maps (BSPM's). By systematic application of the method throughout the cardiac cycle, discriminative spatio-temporal information can be identified. In a second method, a Sebestyen linear transformation (SLT) was derived to give estimates of pairwise, linear separability of clinical classes. The utility of the method was illustrated by the pairwise comparison of 40 normal subjects (NOR), 40 patients with anterior myocardial infarction (AMI), and 40 with inferior myocardial infarction (IMI). The application examples demonstrated that: a) diagnostic information in low potential amplitude regions may surpass that in high amplitude regions, b) probability distributions of characteristic features showed small overlap in NOR versus AMI and NOR versus IMI dichotomies although they were not linearly separable, and c) the single best separating potential sample in the K-S sense for NOR versus AMI or NOR versus IMI dichotomies recovered 88 and 73% of the SLT performance, respectively.     

Nonparametric identification of population models: an MCMC approach

The paper deals with the nonparametric identification of population models, that is models that explain jointly the behavior of different subjects drawn from a population, e.g., responses of different patients to a drug. The average response of the population and the individual responses are modeled as continuous-time Gaussian processes with unknown hyperparameters. Within a Bayesian paradigm, the posterior expectation and variance of both the average and individual curves are computed by means of a Markov Chain Monte Carlo scheme. The model and the estimation procedure are tested on both simulated and experimental pharmacokinetic data.     

Extraction of noise current signatures using wavelets in packaged digital systems

This paper discusses a measurement-based approach for estimating the switching noise current waveform in a functioning computer system. The proposed method consists of a wavelet-based approach for denoising the measured waveform and a technique for capturing the result in an accurate and compact model. The method has been tested on simulated and measured data. The test case considered is a high-speed functioning workstation from Sun Microsystems. Using the current source developed, simultaneous switching noise in the power distribution network of the test system has been simulated with good accuracy     

KCS-new kernel family with compact support in scale space:formulation and impact

Multiscale representation is a methodology that is being used more and more when describing real-world structures. Scale-space representation is one formulation of multiscale representation that has received considerable interest in the literature because of its efficiency in several practical applications and the distinct properties of the Gaussian kernel that generate the scale space. Together, some of these properties make the Gaussian unique. Unfortunately, the Gaussian kernel has two practical limitations: information loss caused by the unavoidable Gaussian truncation and the prohibitive processing time due to the mask size. We propose a new kernel family derived from the Gaussian with compact supports that are able to recover the information loss while drastically reducing processing time. This family preserves a great part of the useful Gaussian properties without contradicting the uniqueness of the Gaussian kernel. The construction and analysis of the properties of the proposed kernels are presented in this paper. To assess the developed theory, an application of extracting handwritten data from noisy document images is presented, including a qualitative comparison between the results obtained by the Gaussian and the proposed kernels.     

具有更高激光功率的新型加工支持系统

在加工制造业，从焊接、切割到粉末金属喷镀，对激光功率的要求正推动二氧化碳激光器机械加工系统向更高的功率水平发展。随着激光光源技术的进步，对有效利用激光功率的要求使机械加工设备支持系统得以同步发展。这些支持系统包括机械运动控制系统、高压辅助气体传递控制系统和高流速切割喷嘴技术等。     

Arc-sine modulation?a method of overcoming nonlinearities in transmission systems

A form of modulation is described which may be used in amplitude nonlinear systems. The signal is a form of phase modulation, but the use of synchronous detection means that it is threshold-free, and certain forms of distortion associated with angle modulation are not present. There is a gain of 6 dB over peak-power-limited a.m. For low-index p.m. systems which are distortion-limited, it may be possible to obtain substantial improvements in signal/noise ratio.