Adaptive transient solution of nonuniform multiconductor transmission lines using wavelets

This paper presents a highly adaptive algorithm for the transient simulation of nonuniform interconnects loaded with arbitrary nonlinear and dynamic terminations. The discretization of the governing equations is obtained through a weak formulation using biorthogonal wavelet bases as trial and test functions. It is shown how the multiresolution properties of wavelets lead to very sparse approximations of the voltages and currents in typical transient analyzes. A simple yet effective time-space adaptive algorithm capable of selecting the minimal number of unknowns at each time iteration is described. Numerical results show the high degree of adaptivity of the proposed scheme.     

On solving first-kind integral equations using wavelets on abounded interval

The conventional method of moments (MoM), when applied directly to integral equations, leads to a dense matrix which often becomes computationally intractable. To overcome the difficulties, wavelet-bases have been used previously which lead to a sparse matrix. The authors refer to “MoM with wavelet bases” as “wavelet MoM”. There have been three different ways of applying the wavelet techniques to boundary integral equations: 1) wavelets on the entire real line which requires the boundary conditions to be enforced explicitly, 2) wavelet bases for the bounded interval obtained by periodizing the wavelets on the real line, and 3) “wavelet-like” basis functions. Furthermore, only orthonormal (ON) bases have been considered. The present authors propose the use of compactly supported semi-orthogonal (SO) spline wavelets specially constructed for the bounded interval in solving first-kind integral equations. They apply this technique to analyze a problem involving 2D EM scattering from metallic cylinders. It is shown that the number of unknowns in the case of wavelet MoM increases by m-1 as compared to conventional MoM, where m is the order of the spline function. Results for linear (m=2) and cubic (m=4) splines are presented along with their comparisons to conventional MoM results. It is observed that the use of cubic spline wavelets almost “diagonalizes” the matrix while maintaining less than 1.5% of relative normed error. The authors also present the explicit closed-form polynomial representation of the scaling functions and wavelets     

Extending multiresolution time-domain (MRTD) technique to the simulation of high-frequency active devices

We present a new time-domain simulation approach for large-signal physical modeling of high-frequency semiconductor devices using wavelets. The proposed approach solves the complete hydrodynamic model, which describes the transport physics, on nonuniform self-adaptive grids. The nonuniform grids are obtained by applying wavelet transforms followed by hard thresholding. This allows forming fine and coarse grids in locations where variable solutions change rapidly and slowly, respectively. A general criterion is mathematically defined for grid updating within the simulation. In addition, an efficient thresholding formula is proposed and verified. The developed technique is validated by simulating a submicrometer FET. Different numerical examples are presented along with illustrative comparison graphs, showing over 75% reduction in CPU time, while maintaining the same degree of accuracy achieved using a uniform grid case. Tradeoffs between threshold values, CPU time, and accuracy are discussed. To our knowledge, this is the first time in the literature to implement and report a wavelet-based hydrodynamic model simulator. This study also represents a fundamental step toward applying wavelets to Maxwell's equations in conjunction with the hydrodynamic model for accurate modeling of high-frequency active devices aiming to reduce the simulation time, while maintaining the same degree of accuracy.     

Numerical investigation of mesh size convergence rate of the finite element method in MESFET simulation

The mesh size convergence rate of the finite element method in two-dimensional GaAs MESFET simulation has been investigated numerically. The equations governing MESFET operation and the finite element formulation of these equations are summarized. The presence of corner singularities at the gate contact endpoints is noteworthy, for such singularities are known to determine the convergence rate in linear model problems. The local potential and electron concentration solutions are obtained in the neighborhood of these singularities and used to estimate a lower bound on the convergence rate for the nonlinear problem. The rate of convergence of the MESFET problem is tabulated for three mesh sequences and discussed. The common source output characteristic of a 0.25 μm gate length GaAs MESFET is calculated and compared to the characteristic of a MESFET fabricated in our laboratory. Considerable discrepancy between the two is obtained; reasons for this are hypothesized.     

Application of biorthogonal interpolating wavelets to the Galerkinscheme of time dependent Maxwell's equations

A family of biorthogonal interpolating wavelets has been applied to time-domain electromagnetic field modeling through the wavelet-Galerkin scheme. The scaling functions are the Deslauriers-Dubuc interpolating functions and the wavelets are the shifted and contracted version of the scaling functions. This set of bases yields a simple algorithm for the solution of Maxwell's equations in time domain due to their interpolation properties. The derivation of the algorithm is presented in this paper, followed by a series of numerical verifications on some resonant structures     

An independently matched parameter SPICE model for GaAs MESFET's

A GaAs MESFET model is presented that addresses the modeling problem arising from the discrepancy between the derivatives of the dc current and the measured small signal parameters of a GaAs MESFET. This discrepancy traditionally required the user of a non-linear circuit analysis program such as SPICE to trade off the accuracy between the dc analysis and ac analysis. This paper addresses this problem and leads to a solution that completely eliminates the need for such a trade off. Two additional nodes are incorporated into the SPICE MESFET model by providing two extra conducting paths necessary to reconcile the aforementioned discrepancies and to keep the equations self-consistent. In addition, the model allows the user to select different sets of model parameters to independently match I_ds, g_m, and g _ds, An integration scheme to transform the new model back to a 3×3 Y-matrix is employed to accelerate the simulation speed     

New wavelet based approach for time domain simulations

A new numerical method for the time domain solution of Maxwell's equations in linear media is proposed in this paper. The field quantities derived from the spatial discretization of Maxwell's equations are expanded in the time domain by wavelets on the interval. This choice yields a new arrangement of the unknowns into a matrix (instead of the usual vector) and transforms the differential equations in time in a Sylvester (1983) matrix equation. The memory requirements are proportional to the number of spatial unknowns and the time evolution of the space quantities is obtained with better accuracy than in conventional marching-on-time techniques.     

Biorthogonal interpolating wavelet with compactly supported duals

In the prevailing design of interpolating wavelets, little attention is paid to wavelets and their duals. The authors construct a new type of interpolating wavelet with compactly supported duals     

Robust fabric defect detection and classification using multiple adaptive wavelets

The wavelet transform has been widely used for defect detection and classification in fabric images. The detection and classification performance of the wavelet transform approach is closely related to the selection of the wavelet. Instead of predetermining a wavelet, a method of designing a wavelet to adapt to the detection or classification of fabric defects has been developed. For further improvement of the performance, the paper extends the adaptive wavelet-based methodology from the use of a single adaptive wavelet to multiple adaptive wavelets. For each class of fabric defect, a defect-specific adaptive wavelet was designed to enhance the defect region at one channel of the wavelet transform, where the defect region can be detected by using a simple threshold classifier. Corresponding to the multiple defect-specific adaptive wavelets, the multiscale edge responses to defect regions have been shown to be more efficient in characterising defects, which leads to a new approach to the classification of defects. In comparison with the single adaptive wavelet approach, the use of multiple adaptive wavelets yields better performance on defect detection and classification, especially for defects that are poorly detected by the single adaptive wavelet approach. The proposed method has been evaluated on the inspection of 56 images containing eight classes of fabric defects, and 64 images without defects. In defect detection, 98.2% detection rate and 1.5% false alarm rate were achieved, and in defect classification, 97.5% accuracy was achieved.     

模拟大规模电路的快速频域小波配置法

提出了一种求解状态方程的方法:频域快速小波配置法.通过将状态方程转入频域求解,并对输出变量直接进行小波展开.这一方法比原有的时域快速小波配置法大大减少了未知变量的数目,从而使计算速度和存储空间都有很大程度的改善.由于小波函数及其反变换均有显式的数学表达式,这一方法在得到频域解析近似解的同时就可以获得时域解析近似解,无须在计算过程中进行耗时的数值积分反变换.同时通过自适应算法的引入,这一方法可以有效提高计算效率.     

M-band biorthogonal interpolating wavelets via lifting scheme

Recently, the lifting scheme was generalized to the multidimensional and multiband cases and was used to design M-band interpolating scaling filters and their duals. Based on this idea, we develop a new lifting pattern, namely, the progressive lifting pattern. This pattern allows us to pairwise generate M-band interpolating filterbanks and wavelets by the order from lowpass to highpass filters. A complete lifting procedure is divided into M - 1 simple steps, in each step, a pair of filters (the l'th filter and its dual) are generated. In this way, an M -band biorthogonal interpolating filterbank/wavelet is determined by M(M - 1) lifting filters. The first 2(M 1) lifting filters completely characterize the two scaling filters as well as the vanishing moments of bandpass and highpass filters; the residual (M - 1) (M - 2) lifting filters are used to pairwise optimize the bandpass and highpass filters in terms of the criterion of stopband energy minimization. The obtained M-band biorthogonal interpolating filterbanks and wavelets provide excellent frequency characteristics, in particular, low stopband sidelobes. Furthermore, the pattern is also utilized to design signal-adapted interpolating filterbanks and their rational coefficient counterparts in terms of subband coding gain. The obtained filterbanks achieve large subband coding gains. The rational coefficient filterbanks preserve the biorthogonality and allow wavelet transforms from integers to integers and a unifying lossy/lossless coding framework at the cost of a slight degradation in subband coding gain.     

Wavelet Denoising for Electric Drives

Signal identification is a common problem in electric drive applications. This paper proposes the use of wavelet transforms to extract and identify specific frequency components. Initially, current measurements from a constant voltage/hertz application are filtered using various wavelets and the results compared with conventional filtering methods. A pseudoadaptive denoising method is then proposed based on wavelets which adjust the level of decomposition depending on the rotor speed. Finally, wavelets are used in a high frequency injection speed estimation scheme and shown to be superior to conventional methods in such cases, where the useful information may be at higher frequency and have imprecise frequency components. Experimental and simulated results verify these statements.     

最优内插的纯二维小波构造

研究了纯二维小波的构造,并根据二维图像各向同性的谱密度模型构造了一组最优内插滤波器,将其用于提升格式中,构造了具有最优内插效果的纯二维小波滤波器组.通过MSE和能量熵实验对比,证明这种纯二维小波滤波器内插效果和能量聚积方面好于或接近于著名Neville滤波器,可以用于图像的压缩和超分辨率.     

Discrete frequency warped wavelets: theory and applications

We extend the definition of dyadic wavelets to include frequency warped wavelets. The new wavelets are generated and the transform computed in discrete-time by alternating the Laguerre transform with perfect reconstruction filterbanks. This scheme provides the unique implementation of orthogonal or biorthogonal warped wavelets by means of rational transfer functions. We show that the discrete-time warped wavelets lead to well-defined continuous-time wavelet bases, satisfying a warped form of the two-scale equation. The shape of the wavelets is not invariant by translation. Rather, the “wavelet translates” are obtained from one another by allpass filtering. We show that the phase of the delay element is asymptotically a fractal. A feature of the warped wavelet transform is that the cut-off frequencies of the wavelets may be arbitrarily assigned while preserving a dyadic structure. The new transform provides an arbitrary tiling of the time-frequency plane, which can be designed by selecting as little as a single parameter. This feature is particularly desirable in cochlear and perceptual models of speech and music, where accurate bandwidth selection is an issue. As our examples show, by defining pitch-synchronous wavelets based on warped wavelets, the analysis of transients and denoising of inharmonic pseudo-periodic signals is greatly enhanced     

Numerical simulation of scattering from rough surfaces: awavelet-based approach

In this paper, a preliminary study is carried out to demonstrate the application of wavelets for improving the computation time and reducing computational memory required for evaluating the statistics of the scattered field from rough surfaces using the method of moments (MoM) in conjunction with a Monte Carlo simulation. In specific, Haar and the first order B-spline wavelet basis functions are applied to the MoM formulation of one-dimensional rough surfaces in order to compare the computation time and sparsity for wavelets in the same family but of higher order. Since the scattering coefficient (the second moment of the backscatter field per unit area) is a gentle function of the surface parameters and the radar attributes, it is demonstrated that a relatively high thresholding level can be applied to the impedance matrix, which leads to a sparser impedance matrix and faster computation time. It is also shown that applying a high threshold level the coefficients of the high-order wavelets would increase out of proportion, however, the effect of these current components averages out when computing the scattering coefficients. The resulting sparse impedance matrices are solved efficiently using fast search routines such as the conjugate gradient method. A systematic study is carried out to investigate the effect of different threshold levels on the accuracy versus computing speed criterion. The computed scattering coefficients are compared to previous results computed using a conventional pulse basis function as well as the existing theoretical solutions for rough surfaces. It is shown that wavelet basis functions provide substantial reductions in both memory requirements and computation time     

基于提升框架的一种自适应滤波方法研究

Haar小波和CDF(2,2)小波都可用提升框架的形式表示,该文把它们与无更新算子的Haar小波有机结合到一起,形成了自适应小波变换,随着信号的变化可以自动地选择合适的小波基。仿真结果表明,自适应小波变换对于含噪声的突变信号和光滑信号都有良好的去噪性能,兼具了Haar小波和CDF(2,2)小波各自的优点,适用范围更宽。     

A wavelet-like filter based on neuron action potentials for analysis of human scalp electroencephalographs

This paper describes the development and testing of a wavelet-like filter, named the SNAP, created from a neural activity simulation and used, in place of a wavelet, in a wavelet transform for improving EEG wavelet analysis, intended for brain-computer interfaces. The hypothesis is that an optimal wavelet can be approximated by deriving it from underlying components of the EEG. The SNAP was compared to standard wavelets by measuring Support Vector Machine-based EEG classification accuracy when using different wavelets/filters for EEG analysis. When classifying P300 evoked potentials, the error, as a function of the wavelet/filter used, ranged from 6.92% to 11.99%, almost twofold. Classification using the SNAP was more accurate than that with any of the six standard wavelets tested. Similarly, when differentiating between preparation for left- or right-hand movements, classification using the SNAP was more accurate (10.03% error) than for four out of five of the standard wavelets (9.54% to 12.00% error) and internationally competitive (7% error) on the 2001 NIPS competition test set. Phenomena shown only in maps of discriminatory EEG activity may explain why the SNAP appears to have promise for improving EEG wavelet analysis. It represents the initial exploration of a potential family of EEG-specific wavelets.     

An equalization algorithm for wavelet packet based modulationschemes

A considerable amount of attention has been given in the literature to the use of wavelets for modulation and equalization. In this correspondence, we present an equalization algorithm for a wavelet packet-based modulation scheme. A nonideal channel can be divided into a set of bands, where each band can be approximated as a simple attenuation and delay channel. Wavelet packets, being narrowband and orthonormal, are a natural choice for realizing such bands. Thus, if the data sequence is used to modulate a set of wavelet packets, the equalization problem reduces to that of determining the delay introduced by the channel for each of the wavelet packets (if the wavelet packets do not overlap in the frequency domain) and possibly a change of sign in the decoded symbols. The attenuation affects the SNR at the output of the demodulator, which in turn affects the correct decoding of the transmitted symbols. A minimum square variance algorithm for adaptively choosing the delay has been proposed. The algorithm uses the statistics of the received sequence to pick the appropriate delay. Simulations have been conducted to study the performance of the equalization algorithm and compare it with that of DFT-based DMT scheme     

A multiresolution study of two-dimensional scattering by metalliccylinders

The application of wavelet transforms in method of moments (MoM) solutions for scattering problems is extended to cases involving metallic cylinders whose periphery contains a variety of length-scale features ranging from smoothly varying large-scale features (characterized by a radius of curvature of several wavelengths) to rapidly varying small scale ones (characterized by a radius of curvature that is small compared with the wavelength). The basic idea is to first consider a periodic extension of the equivalent current in the arc-length variable with a period identical to the scatterer circumference, and then to expand this representation using a set of periodic wavelets derived from a conventional basis of wavelets by a periodic extension. Using a Galerkin method and subsequently applying a threshold operation, a substantial reduction in the number of elements of the moment-method matrix is attained without virtually affecting the solution accuracy. The proposed extension is illustrated by a numerical analysis of TM (transverse magnetic) and TE (transverse electric) scattering from a cylinder of elliptic cross section. A thorough study is carried out showing how the solution accuracy improves with increasing resolution level, and how this accuracy is affected by a thresholding process which renders the moment matrix sparsely populated     

A higher order parallelized multilevel fast multipole algorithm for3-D scattering

A higher order multilevel fast multipole algorithm (MLFMA) is presented for solving integral equations of electromagnetic wave scattering by three-dimensional (3-D) conducting objects. This method employs higher order parametric elements to provide accurate modeling of the scatterer's geometry and higher order interpolatory vector basis functions for an accurate representation of the electric current density on the scatterer's surface. This higher order scheme leads to a significant reduction in the mesh density, thus the number of unknowns, without compromising the accuracy of geometry modeling. It is applied to the electric field integral equation (EFIE), the magnetic field integral equation (MFIE), and the combined field integral equation (CFIE), using Galerkin's testing approach. The resultant numerical system of equations is then solved using the MLFMA. Appropriate preconditioning techniques are employed to speedup the MLFMA solution. The proposed method is further implemented on distributed-memory parallel computers to harness the maximum power from presently available machines. Numerical examples are given to demonstrate the accuracy and efficiency of the method as well as the convergence of the higher order scheme