Conformal hybrid finite difference time domain and finite volumetime domain

A hybrid method that combines the finite difference time domain (FDTD) and the finite volume time domain (FVTD) methods is presented. The FVTD, based on a conformal and unstructured grid is used in the near vicinity of the surface of a scatterer, and the FDTD is used to model the fields in the surrounding area. The two are coupled together through interpolation. The vertex-based FVTD allows for more convenient and accurate interpolations than a conformal FDTD method. The hybrid method is validated through two examples-the scattering by a PEC cube and sphere-by comparison with the direct FDTD solution, and with an exact Mei series solution for the spherical case     

A modified finite element method for analysis of finite periodicstructures

A modified finite element method with new solving algorithm is proposed to analyze electromagnetic problems of finite periodic structures. Dielectric-loaded parallel-plate waveguides with rectangular and triangular dielectric gratings are tackled as an example of the present approach. Numerical results are checked by the self-convergence test and by comparing with those obtained by other methods. Finally, the dependence of the scattering parameters on the frequency, the period number, and the grating height is analyzed and compared     

Recursive realization of finite impulse filters using finite field arithmetic

Recursive filter design techniques are described and developed for finite impulse filters using finite field arithmetic. The finite fields considered have the formGF(q^{2}), the Galois field ofq^{2}elements, and are analogous to the field of complex numbers whenqis a prime such that(-1)is not a quadratic residue. These filters can be designed to yield either a desired finite impulse or finite frequency response function. This filtering technique has other possible applications, including the encoding or decoding of information and signal design. Infinite signal trains can be decomposed naturally into orthogonal sequences which may be useful in the encoding and decoding process and may provide another approach to convolutional coding. Since the recursive filters developed here do not have the accumulation of round-off or truncation error that one might expect in recursive computations, such filters are noise-free transducers in the sense of Shannon.     

用混合有限体积/有限元法研究尾焰对太阳辐射的吸收问题

为掌握卫星姿控推进器尾焰的吸收特性,研究了尾焰对太阳红外辐射的吸收问题。在直角坐标系下,建立了尾焰对太阳红外辐射的吸收模型,并采用混合有限体积/有限元法计算太阳光线经过尾焰吸收后的光谱辐射亮度。该方法使用有限元法进行角度离散,有限体积法进行空间离散;对每一个控制体,可同时耦合求出所有角度方向的辐射亮度。通过求解,得到了受到尾焰吸收后的太阳光谱辐射亮度和尾焰的光谱吸收率。以传递方程积分法的计算结果作为基准解,对比分析了有限体积法和混合有限体积/有限元法产生射线效应的强弱程度。通过分析可知:在某些波段上,太阳辐射受到尾焰的吸收程度较强;与有限体积法的计算结果相比,混合有限体积/有限元法的计算结果与基准解之间的差异相对较小。以上结果表明:混合有限体积/有限元法的计算精度较高,并能够较好地降低射线效应。     

Hypothesis testing with finite memory in finite time (Corresp.)

The hypothesis-testing problem has recently been studied under a finite-memory constraint. However, most work has been concerned with the large-sample theory. Here we study the small-sample theory for binary-valued observations.     

On tests with finite memory in finite time (Corresp.)

The purpose of this correspondence is to display an inductive proof of an optimality result for testing symmetric simple hypotheses concerning a binomial parameter with a three-state memory andnobservations. Specifically, it is shown that if one restricts attention to three-state automata allowing transitions only between adjacent states, then no artificial randomization is required in the middle state of the optimal machine. The success in this problem of what will be called simultaneous induction suggests the possibility of obtaining characterizations of optimal automata in more general problems by similar techniques.     

Unsupervised learning and the identification of finite mixtures

The first portion of this paper is tutorial. Beginning with a standard definition of an abstract pattern-recognition machine, "learning" is given a mathematical meaning and the distinction is made between supervised and unsupervised learning. The bibliography will help the interested reader retrace the history of learning in pattern recognition. The exposition now focuses attention on unsupervised learning. Carefully, it is explained how problems in this subject can be viewed as problems in the identification of finite mixtures, a statistical theory that has achieved some maturity. From this vantage point, it is demonstrated that identification theory implies unsupervised learning is possible in many important cases. The remaining sections present a general method for achieving unsupervised learning. Other authors have proposed schemes having greater computational convenience, but no method previously published is as inclusive as the one revealed here, which we demonstrate to be effective for all the many cases wherein unsupervised learning is known to be possible.     

On the size requirement for finite phased-array models

The question considered is how large an array model must be in order to capture approximately the characteristics of both the interior and the edge elements of a large multi-octave phased array. Arrays with tapered slot elements and with top-loaded dipoles are analyzed at element spacings as small as 0.1λ and it is concluded that at any frequency, a finite array model with this type of element should be at least 5λ×5λ in size. This suggests the generalization of the 10×10 element model often used as an engineering "rule of thumb" in the normal narrow-band case with 0.5λ element spacing. An array model with a 5:1 bandwidth thus needs about 25 times more elements than a narrow-band model. The array feed impedance is considered and it is found that the array active reflection coefficient in finite arrays but not in infinite arrays is dependent on the matching condition at the feed. The finite-difference time-domain (FDTD) technique is used to analyze arrays up to 49×49 elements, demonstrating that computer power now makes feasible the full wave solution for large phased arrays with complex geometry     

On the connectivity in finite ad hoc networks

Connectivity and capacity analysis of ad hoc networks has usually focused on asymptotic results in the number of nodes in the network. In this letter we analyze finite ad hoc networks. With the standard assumption of uniform distribution of nodes in [0, z], z > 0, for a one-dimensional network, we obtain the exact formula for the probability that the network is connected. We then extend this result to find bounds for the connectivity in a two-dimensional network in [0, z]²     

Efficient computation of the delay-optimized finite length MMSE-DFE

We present new fast algorithms for computing the optimum settings of a finite-length minimum-mean-square-error decision feedback equalizer (MMSE-DFE) from channel and noise estimates. These algorithms are based on displacement structure theory and generalize the algorithms of Al-Dhahir and Cioffi (see ibid., vol.43, no.11, 1995) by including delay optimization. Both symbol-spaced and fractionally spaced feedforward filters are considered     

Codes on finite geometries

New algebraic methods for constructing codes based on hyperplanes of two different dimensions in finite geometries are presented. The new construction methods result in a class of multistep majority-logic decodable codes and three classes of low-density parity-check (LDPC) codes. Decoding methods for the class of majority-logic decodable codes, and a class of codes that perform well with iterative decoding in spite of having many cycles of length 4 in their Tanner graphs, are presented. Most of the codes constructed can be either put in cyclic or quasi-cyclic form and hence their encoding can be implemented with linear shift registers.     

Estimation with finite memory

A finite-state model for sequential minimum-mean-square-error estimation of a random variable in additive noise is analyzed to determine the dependence of optimum performance and structure on the memory size of the estimator. Necessary conditions for determining the structure of the optimum finite-state estimator are derived for arbitrary statistics. Numerical results are presented for Gaussian statistics. The performance of several different estimators is used to show the trade-off one may obtain between memory size, observation quality, and number of observations.     

A finite difference approach to the wire junction problem

An approach to treating the thin-wire junction geometry, which arises in the computer modeling of a great many electromagnetic radiation and scattering problems, is presented. The method is based upon a finite-difference type interpretation of the differential operator in the Pocklington form of the integro-differential equation representing the junction problem. An important advantage of the method is that it is capable of producing accurate results even with relatively simple basis and testing functions, e.g., pulse anddelta-functions. Furthermore, the method does not require the imposition of additional constraints, such as the Kirchhoff current law or the conservation of charge, at the junction points. The method is versatile in that it applies to L-shaped structures as well as to junctions of thin wires of dissimilar radii. Numerical results based on the present finite difference approach have been computed and good agreement with results derived by other independent methods has been observed. An important conclusion of this work is that the conventional interpretation of the differential operator leads to erroneous results since the sampling interval in the conventional finite difference scheme is different from the correct value of the sampling interval found in this paper.     

Image encryption based on the finite field cosine transform

In this paper, a novel image encryption scheme is proposed. The technique involves two steps, where the finite field cosine transform is recursively applied to blocks of a given image. In the first step, the image blocks to be transformed result from the regular partition of subimages of the original image. The transformed subimages are regrouped and an intermediate image is constructed. In the second step, a secret-key determines the positions of the intermediate image blocks to be transformed. Besides complying with the main properties required by image encryption methods, the proposed scheme provides benefits related to computational complexity and encoding of the ciphered-images.     

Optimization of planar devices by the finite element method

The finite-element method is an efficient and flexible way of computing the scattering parameters of N-port planar devices (microstrip, stripline, rectangular waveguide, etc.). In addition, it can provide, at little extra cost, the sensitivity of scattering parameters to changes in the shape of the device. such information can lead to a faster automatic optimization of the shape. This approach has been implemented with high-order, triangular finite elements and the Broyden-Fletcher-Goldfarb-Shanno optimization scheme. Sensitivities were computed for an empty parallel-plate waveguide and for a rectangular waveguide containing a dielectric slab. The agreement with analytical solutions was excellent. The method was used to determine the optimum shape of a microstrip 3-dB hybrid and was found to require far fewer analyses than a previous technique     

On finite word length effects for the FIR MMSE-DFE

An analytical upper bound on the degradation in the decision-point signal-to-noise ratio (SNR) of the finite-impulse-response (FIR) minimum mean-square error decision-feedback equalizer (MMSE-DFE) due to finite-precision implementation of its optimum filter coefficients is derived. Simulation results demonstrate the tightness of the analytical bound for scenarios of most practical interest     

Modal fields calculation using the finite difference beampropagation method

A method is described to construct modal fields for an arbitrary one- or two-dimensional refractive index structure. An arbitrary starting field is propagated along a complex axis using the slowly varying envelope approximation (SVEA). By choosing suitable values for the step-size, one mode is maximally increased in amplitude on propagating, until convergence has been obtained. For the calculation of the next mode, the mode just found is filtered out, and the procedure starts again. The method is tested for one-dimensional refractive index structures, both for nonabsorbing and for absorbing structures, and is shown to give fast convergence     

Efficient interface conditions for the finite difference beampropagation method

It is shown that by adapting the refractive indexes in the vicinity of interfaces, the 2-D beam propagation method based on the finite-difference (FDBPM) scheme can be made much more effective. This holds especially for TM modes propagating in structures with high-index contrasts, such as surface polaritons. A short discussion is given on the applicability of the FDBPM     

On the monotone finite difference schemes for energy transportmodels

The success of numerical simulation is determined by the stability of discretization schemes. The existing schemes for the energy transport (hydrodynamic-like) models are examined in terms of the maximum principle. Improved finite difference schemes are developed for the current continuity and energy balance equations