A hybrid equation approach for the solution of electromagneticscattering problems involving two-dimensional inhomogeneous dielectriccylinders

A numerical procedure for the solution of electromagnetic scattering problems involving inhomogeneous dielectric cylinders of arbitrary cross section is discussed. The cases of illumination by both transverse magnetic (TM) and transverse electric (TE) plane waves are considered. The scattering problems are modeled via a hybrid integral-equation/partial-differential-equation approach. The method of moments is applied to obtain a system of simultaneous equations that can be solved for the unknown surface current densities and the interior electric field. The interior region partial differential equation and the exterior region surface integral equation are coupled in such a manner that many existing surface integral equation computer codes for treating problems involving scattering by homogeneous dielectric cylinders can be modified easily to generate the block of the matrix corresponding to the surface current interactions. The overall system matrix obtained using the method of moments is largely sparse. Numerical results are presented and compared with exact solutions for homogeneous and inhomogeneous circular cylinders     

T矩阵递推算法用于二维混合目标RCS计算

利用递推算法计算任意形状二维导体加介质体目标的电磁散射。建立导体部分单独存在时的T矩阵，对于内谐振频率点上生成的病态矩阵用奇异值分解方法解决，用广义递推算法求出有耗介质单体T矩阵。然后采用二体散射的方法求得总散射场。计算结果表明了该方法的正确性。     

A comparative study of the OSRC approach in electromagneticscattering

A technique referred to as the on-surface radiation boundary condition (OSR) approach is applied to a variety of two-dimensional imperfectly conducting geometries. Specifically, analytical solutions and numerical data are presented for the scattering by elliptical and rectangular cylinders and restrictive strips. These are then compared with calculations using the traditional physical optics (PO) approximation and moment method (MM). Emphasis is on the accuracy afforded by using OSRC as opposed to the MM or PO formulations     

A T-matrix approach for EM scattering by a perfectly conducting periodic surface

The novel use of a Fourier exponential representation of the field induced on a perfectly conducting periodic surface is shown to yield a T-matrix which is numerically stable for deeply corrugated surfaces. Whereas the Rayleigh hypothesis limited the maximum slope of the surface to less than 0.448 in Waterman's original T-matrix scheme [1], our T-matrix is applicable even when the maximum slopes are of the order of 1.5.     

A potential integral equations method for electromagneticscattering by penetrable bodies

A method for computing the electromagnetic scattering by general inhomogeneous penetrable bodies is presented. The method is based on the volume equivalence principle and it uses the electromagnetic potentials as unknowns. The resulting coupled integral equations system is solved by the method of moments in combination with cubical and curvilinear meshes in the special case of purely dielectric scatterers. To show the accuracy of the method, numerical results of the transmitted and of the scattered fields are compared with existing analytical and experimental results     

A recursive approach to signal detection

The classical problem of detecting known signals in additive nonstationary nonwhite noise is treated using state-variable methods. The noise is assumed to be generated as the solution of a linear time-varying differential equation driven by white noise. The Markov property of the noise is used to derive a difference equation for the likelihood ratio. The terms in the difference equation are given directly in terms of the coefficients of the differential equation defining the noise. These results, being in recursive form, reduce considerably the computational effort when discrete samples are used. The signal-to-noise ratio is also derived. Explicit expressions for the likelihood ratio are also obtained for continuous processing. These results are given directly in terms of the signals and the noise-generating equation. Thus, there are no integral equations to solve. The signal-to-noise ratio is calculated explicitly for both stationary and nonstationary noise.     

A novel approach for stabilizing recursive least squares filters

A novel approach for stabilizing recursive least squares (RLS) filters is presented. The approach relies on a detailed fixed point analysis, which provides two important benefits. The analysis reveals a bias in the error propagation mechanism, providing an analytical basis for instability problems. The analysis then indicates which specific roundoff errors are causing instability. These roundoff errors are then biased in such a way that the overall filter is biased towards stable performance. Experimental results indicate that stability can be achieved with negligible loss in least squares performance     

A recursive robust filtering approach for 3D registration

This work presents a new recursive robust filtering approach for feature-based 3D registration. Unlike the common state-of-the-art alignment algorithms, the proposed method has four advantages that have not yet occurred altogether in any previous solution. For instance, it is able to deal with inherent noise contaminating sensory data; it is robust to uncertainties caused by noisy feature localisation; it also combines the advantages of both \(L_\infty \) and \(L_2\) norms for a higher performance and a more prospective prevention of local minima. The result is an accurate and stable rigid body transformation. The latter enables a thorough control over the convergence regarding the alignment as well as a correct assessment of the quality of registration. The mathematical rationale behind the proposed approach is explained, and the results are validated on physical and synthetic data.     

A recursive approach to low complexity codes

A method is described for constructing long error-correcting codes from one or more shorter error-correcting codes, referred to as subcodes, and a bipartite graph. A graph is shown which specifies carefully chosen subsets of the digits of the new codes that must be codewords in one of the shorter subcodes. Lower bounds to the rate and the minimum distance of the new code are derived in terms of the parameters of the graph and the subeodes. Both the encoders and decoders proposed are shown to take advantage of the code's explicit decomposition into subcodes to decompose and simplify the associated computational processes. Bounds on the performance of two specific decoding algorithms are established, and the asymptotic growth of the complexity of decoding for two types of codes and decoders is analyzed. The proposed decoders are able to make effective use of probabilistic information supplied by the channel receiver, e.g., reliability information, without greatly increasing the number of computations required. It is shown that choosing a transmission order for the digits that is appropriate for the graph and the subcodes can give the code excellent burst-error correction abilities. The construction principles     

A new approach to recursive Fourier transform

In the recursive Fourier transform, the data window can be chosen such that the number of computations required to update the transform at each frequency upon reception of a new data sample is independent of the transform block length.     

A recursive approach for enumerating minimal cutsets in a network

This paper presents a new recursive labelling algorithm for determining all minimal cutsets in a directed network, using an approach adapted from dynamic programming algorithms for the classical shortest route problem. The algorithm produces all minimal cutsets, and uses comparison logic to eliminate any redundant cutsets. Computational experience shows that: (1) the time per cutset varies linearly with the number of nodes but decreases exponentially with the density of the graph; and (2) whereas the algorithm's performance with regard to `change in the time per cutset vs. the number of nodes' is similar to other algorithms, it appears to exhibit superior performance where the time/cutset is compared to the density of the graph     

A recursive soft-decision approach to blind image deconvolution

This paper presents a new approach to blind image deconvolution based on soft-decision blur identification and hierarchical neural networks. Traditional blind algorithms require a hard-decision on whether the blur satisfies a parametric form before their formulations. As the blurring function is usually unknown a priori, this precondition inhibits the incorporation of parametric blur knowledge domain into the restoration schemes. The new technique addresses this difficulty by providing a continual soft-decision blur adaptation with respect to the best-fit parametric structure throughout deconvolution. The approach integrates the knowledge of well-known blur models without compromising its flexibility in restoring images degraded by nonstandard blurs. An optimization scheme is developed where a new cost function is projected and minimized with respect to the image and blur domains. A nested neural network, called the hierarchical cluster model is employed to provide an adaptive, perception-based restoration. Its sparse synaptic connections are instrumental in reducing the computational cost of restoration. Conjugate gradient optimization is adopted to identify the blur due to its computational efficiency. The approach is shown experimentally to be effective in restoring images degraded by different blurs.     

微元法计算粒子光散射的T矩阵

粒子的光散射是光学检测中的一个重要内容.T矩阵方法被广泛地应用于粒子的光散射计算中.在计算T矩阵的方法中,最流行的方法称之为扩展边界法(EBCM),但是它很大的程度上只适合轴对称和近似球形的粒子.提出了一种新的计算T矩阵的方法.将积分式直接作用在粒子表面,粒子表面进行三角形网格化,并通过三角形网格将积分转换为求和.这种方法能够计算非轴对称甚至接近真实形状粒子的光散射.     

Novel BI-FDTD approach for the analysis of chiral cylinders and spheres

A versatile time-domain technique, known as bi-isotropic finite difference time domain (BI-FDTD), has recently been introduced for the numerical analysis of electromagnetic wave interactions with complex bi-isotropic media. However, to date only one-dimensional BI-FDTD schemes have been successfully implemented. This paper presents novel two-dimensional (2-D) and three-dimensional (3-D) dispersive BI-FDTD formulations for the first time. The update equations for these new 2-D and 3-D BI-FDTD approaches are developed and applied to the analysis of electromagnetic wave scattering by chiral cylinders and spheres in free space. The distinctive feature of this technique is the use of two independent sets of wavefields representing the left- and right-polarized waves in the chiral medium. This wavefield decomposition approach allows dispersive models for the chirality parameter as well as the permittivity and permeability of the medium to be readily incorporated into an FDTD scheme. The 2-D and 3-D BI-FDTD simulation results are compared with available analytical solutions for the scattering from a circular chiral cylinder and a chiral sphere respectively.     

A recursive free-body approach to computer simulation of human postural dynamics

A recursive, free-body approach to the estimation of joint torques associated with observed motion in linkage mechanisms has recently been shown to be computationally more efficient than any other known approach to this problem. This paper applies this method to the analysis of human postural dynamics and shows how it can also be used to compute accelerations for specified joint torques. The latter calculation, referred to here as the direct dynamics problem, has until now involved symbolic complexity to such an extent as to generally limit computer simulation studies of postural control to very simple models. The model presented in this paper is both straightforward and general, and removes this obstacle to the investigation of possible neural control mechanisms by means of computer simulation. A computationally oriented linearization procedure for the direct dynamics problem is also included in the paper. Finally, example simulation results and corresponding measured body motions for human subjects are presented to validate the method.     

An incremental `add-on' approach to determining the effect ofmodification of the geometry of a thin plate on its electromagneticscattering properties

The problem of rapid estimation of the effect of perturbing a thin plate structure is addressed using the add-on technique that was introduced recently by R. Kastner (see ibid., vol.37, p.353-61, 1989). An important feature of this method is its ability to make efficient use of previously computed results for the current distribution on a portion of the scatterer that remains unchanged as the geometry of the plate is modified. The procedure, which has been successfully applied to large irregular strip arrays and to a class of planar geometries that introduce negligible cross-polarization effects in the scattering process, is extended in this work to apply to arbitrary plates. In order to demonstrate the versatility of the method, numerical results are given for a number of plate geometries, including one with apertures     

On the recursive solution of the normal equations of bilateralmultivariate autoregressive models

A multivariate version of the bilateral autoregressive (AR) model is proposed, and a recursive algorithm is presented to solve the normal equations of the bilateral multivariate AR models. The recursive algorithm is computationally efficient and easy to implement as a computer program. The recursive algorithm is useful for identifying and smoothing not only bilateral multivariate AR processes but multidimensional multivariate AR processes and multivariate spatio-temporal processes as well     

A recursive frequency-sampling method for designing zero-phase FIRfilters by nonuniform samples

A novel frequency-sampling method for designing zero-phase FIR filters from nonuniform samples is presented. The method is fast, simple, recursive and can be used in the design of 1D or 2D zero-phase FIR filters by imposing some mild constraints on sample locations in the 2D frequency plane. Based on a novel Newton representation of the filter transfer function the proposed method guarantees real results, saves a number of operations and produces accurate solutions even in cases of designing high-order filters or when the interpolation matrix is ill-conditioned. In the progressive case when the next sample appears, the design parameters are evaluated by updating the old ones with correction terms that could be used as indicators for convergence, approximation, or filter reduction. The method can be used in mD filter design, in LU-factorization or in inversion of cosine matrices     

A recursive algorithm for the error probability evaluation of M-QAM

A general recursive algorithm for the efficient and accurate computation of the bit error rate (BER) of square-shaped M-QAM constellations over additive white Gaussian noise (AWGN) channels is derived. We take advantage of the relationship amongst different square-shaped M-QAM constellations using Gray coded bit mapping     

A recursive MISD architecture for pattern matching

Many applications require searching for multiple patterns in large data streams for which there is no preprocessed index to rely on for efficient lookups. An multiple instruction stream-single data stream (MISD) VLSI architecture that is based on a recursive divide and conquer approach to pattern matching is proposed. This architecture allows searching for multiple patterns simultaneously. The patterns can be constructed much like regular expressions, and add features such as requiring subpatterns to match in a specific order with some fuzzy distance between them, and the ability to allow errors according to prescribed thresholds, or ranges of such. The current implementation permits up to 127 simultaneous patterns at a clock frequency of 100 MHz, and does 1.024/spl times/10/sup 11/ character comparisons per second.