A Polynomial Method for Fitting Continuous Distributions of Exponentials with Positivity Constraint

The need to fit sums of decaying exponentials to data is ubiquitous in the life sciences, where biological systems are often modeled as collections of interconnected compartments. When the number of compartments is extremely large, it becomes more appropriate to consider the data concerned as the integral of a continuous distribution of exponentials. A method is presented for determining distributions of exponentials from data which can be implemented on a personal computer. The technique, termed the "polynomial method," assumes that the distributions are smooth and slowly varying and can be represented by a low-order polynomial. An iterative addition to the technique is also described that allows positive distributions to be recovered, should this be appropriate. The technique is applied to simulated data and to relaxed expiration volume data obtained from dogs.     

Time-domain techniques in the singularity expansion method

New methods of determining the natural frequencies and natural modes of a structure as characterized in the singularity expansion method (SEM) are presented. The method is based on the time-domain scattering equation which can be east in the form of a matrix difference equation. The homogeneous solution of the difference equation is a series of exponentials as found in the SEM representation. The natural frequency and mode solutions may be obtained either from the determinant of a matrix sum, which is similar to the current frequency-domain search method, or by an eigenvalue approach as in systems theory. The latter has shown promise for efficient SEM computations. An example of each approach is presented.     

Efficient representation of induced currents on large scatterersusing the generalized pencil of function method

It is shown that the currents induced over large and smooth scatterers can often be represented by a series of complex exponentials with only a few terms. The generalized pencil of function method is employed to extract these exponentials from the numerical solution of the scattering problem derived by using the method of moments. Illustrative examples include a partially-coated two-dimensional scatterer modeling a helicopter blade and the three-dimensional problem of scattering by a thin plate. The ultimate objective of this effort is to solve a class of large-body scattering problems, for arbitrary angles of incidence including the grazing angle, by utilizing the numerically-derived, complex exponential type of basis functions extrapolated to higher frequencies. It is well known that the physical optics approximation for the induced current becomes inaccurate when the angle of incidence is close to grazing, and the asymptotic methods, e.g., the GTD can become unwieldy for scatterers with edge treatments and those with complex geometrical shapes. The approach based upon the use of numerically derived entire domain basis functions on a portion of the body is proposed as a means to circumventing this difficulty     

Scattering from a finite array of microstrip patches

A full-wave solution to the problem of plane wave scattering by a finite array of rectangular microstrip patches printed on a grounded dielectric slab is presented. The electric field integral equation is solved using the spectral-domain Green's function/moment method approach. Derivations for the elements of the impedance and voltage matrices are presented. An efficient massively parallel computer implementation of the moment method solution is described. Computed radar cross section (RCS) data for microstrip patch antenna arrays are presented as a function of incident signal frequency and angle of incidence     

Prony and Polynomial Approximations for Evaluation of the Average Probability of Error Over Slow-Fading Channels

A novel and simple semianalytical method for evaluating the average probability of transmission error for digital communication systems that operate over slow-fading channels is presented. The proposed method applies a sum of exponentials fit known as the Prony approximation to the conditional probability of error. Hence, knowledge of the moment-generating function of the instantaneous signal-to-noise ratio (SNR) at the detector input can be used to obtain the average probability of error. Numerical results show that knowledge of the conditional probability of error at only a small number of points and the sum of only two exponentials are sufficient to achieve very high accuracy; the relative approximation error of the exact average probability of error is less than 6% in most of the cases considered. Furthermore, a piecewise polynomial approximation of the conditional probability of error is investigated as an alternative to the sum of exponentials fit. In this case, knowledge of the partial moments of the instantaneous SNR at the detector input can be used to obtain the average probability of error. Numerical results indicate that, to achieve good accuracy, the method based on the polynomial approximation requires that the product of the polynomial degree and the number of approximation subintervals be larger than 10.      

Adaptive channel partitioning and modulation for linear time-varying channels

We present a novel channel partitioning and modulation technique for linear time-varying (LTV) channels using adaptive bases of localized complex exponentials. We show that localized complex exponentials are approximate eigenfunctions of underspread LTV channels. A basis of localized complex exponentials that approximately diagonalizes the LTV channel is selected adaptively by the receiver during a training period. The basis selection process is equivalent to matching the support intervals of the localized complex exponentials to the rate of the channel time variation. The receiver sends information regarding the selected basis to the transmitter which modulates the subsequent data stream in this basis. The adaptive modulation technique performs significantly better than conventional orthogonal frequency-division multiplexing systems for rapidly varying LTV channels such as time-frequency-selective mobile radio channels.     

Reconstruction of the amplitude-phase distribution of the field of the received signal in the aperture of a phased antenna array from the measured power

A method for solution of a complex scientific and engineering problem, which is known as the phase problem, is proposed. The phase problem is the problem of reconstruction of the amplitude-phase distribution of the signal field over the receiving aperture from the measured power. The solution is presented for a phased antenna array.     

Analysis of a coaxially fed monopole in a rectangular waveguide

The boundary-value problem of a coaxially fed monopole in a rectangular waveguide is solved. The technique of image method is applied to transform the original problem into an equivalent problem. A fast convergent series solution based on the Fourier transform and mode matching is presented. Our computation results compare favorably with other existing data.     

Generalization of the ECCS method to the multihour case

The classical ECCS method for dimensioning hierarchical telephone networks is extended to the multihour case. The problem is reformulated as a nonlinear optimization method, and the Kuhn-Tucker equations are derived. It is shown why the ECCS method cannot solve this multihour case. The ECCS method is presented as a solution technique for the Lagrangian relaxation of the multihour problem in which subgradient techniques are used for the solution of the dual. A numerical algorithm implementing these ideas is described that can handle networks with arbitrary hierarchies and allows time-of-day routing changes. Preliminary numerical results of the method are presented, showing that the multihour algorithm can reduce a network's cost when compared to currently used methods     

Waveguides of Arbitrary Cross Section by Solution of a Nonlinear Integral Eigenvalue Equation

The problem of electromagnetic wave propagation in hollow conducting waveguides of arbitrary cross section is formulated as an integro-differential equation in terms of fields at the waveguide boundary. Cutoff wave numbers and wall currents appear as eigenvalues and eigenfunctions of a nonlinear eigenvalue problem involving an integro-differential operator. A variational solution is effected by reducing the problem to matrix form using the method of moments. A specific solution of the problem is developed using triangle expansion functions in the method of moments. The solution is simplified by symmetry considerations and is implemented by two digital computer programs. Listings and full documentation of these programs are available. This solution yields accurate determinations of cutoff wave numbers, wall currents, and distributions of both longitudinal and transverse modal field components for the first several modes. Illustrative computations are presented for the single-ridge waveguide, which has a complicated boundary shape that does not lend itself to exact solution.     

A remark on the computation of Fock functions for negative arguments

The Fock functions are mainly used in diffraction theory. A problem with some of these functions is that accurate numerical computation of integrals with certain exponentials is needed. An integration contour that essentially solves this problem is discussed.     

Application of the multilevel single-linkage method toone-dimensional electromagnetic inverse scattering problem

An inverse scattering method for the reconstruction of the permittivity and conductivity profiles of a multilayered medium and for that of the impedance profile of a nonuniform transmission line is proposed. The inversion is based on the global minimization of an objective function by the multilevel single-linkage method. The objective function is defined as the mean-square error between the measured data and the data obtained from the solution of the forward problem. An exact formulation for the gradient of the objective function in closed form is derived. The necessary condition for the unique solution of the inverse problem of a nonuniform transmission line is discussed. Reconstruction examples using both experimental and noisy synthetic data are presented     

区域分解时域有限差分方法(DD-FDTD)及其在散射问题中的应用

本文提出一种区域分解的时域有限差分算法(DD-FDTD).依据待解问题的特点,把待解问题分解为几个子区域,在各个子区域中,采用适合于该区域的共形网格进行划分计算,通过一种有效的信息传递方案,把各个子区域综合起来,获得原问题的解.通过采用这种方法,一个复杂的问题可以得到简化,从而变得适于求解,同时,共形网格和精确的信息传递方案的使用,大幅度提高了计算精度.文中,用该算法对二维电磁散射问题进行了分析计算,获得了精确的计算结果.     

Limited angle reconstruction using stabilized algorithms

The stability of solutions to the limited-angle tomography reconstruction problem obtained by using the projections-onto-convex-sets (POCS) technique are examined. Although POCS techniques provide a feasible solution to the reconstruction problem, the solution is only one sample from the intersection of the closed convex sets that define the solution space. A method for evaluating the ensemble of possible solution waveforms that are in the neighborhood of a solution is presented. The ensemble characteristics are used to construct an inverse filter which is then applied to the computed solution. The results obtained using this method are less sensitive to noise amplification and are less dependent on both starting data and the number of iterations. An estimate of the object-dependent extrapolation that is possible using either linear or nonlinear constraints is provided.     

The Magnetic Field Problem And the Analytical Continuation of the Magnetic Field for Two-Dimensional, Homogeneously And Inhomogeneously Magnetized Bodies

A method is presented for the calculation of the magnetic field strength inside as well as outside a homogeneously or inhomogeneously magnetized two-dimensional body. Employing Strahov's solution for the field problem of a homogeneously magnetized body, a complete solution can be found for the external field of the body only. The calculation scheme developed here agrees with the relations given for this problem by Kolbenheyer and Tolcsvay, but it is more readily applicable to the solution of the inverse problem where the magnetization shall be calculated from the measured magnetic field. On the basis of the proposed calculation method a technique is described for the analytical continuation of the outer magnetic field into the inner region of a two-dimensional magnetized body. Several examples illustrate the application of the presented methods.     

Analysis of diffraction of a plane wave and of the field of a point source by a multirow grating

A multirow grating of impedance or dielectric elements is considered. The 2D problem of scattering by such a grating is solved with the help of the modified null field method and the pattern equation method. A system of integral equations is derived and the reflection and transmission coefficients are determined as functions of various parameters of the problem. The excitation of the grating by a current filament is investigated. An asymptotic solution is obtained for the case when the periods of the grating rows and interrow distances are rather large. In the low-frequency approximation, a solution to the problem for a grating of circular cylinders is presented.     

Universal composite hypothesis testing: a competitive minimaxapproach

A novel approach is presented for the long-standing problem of composite hypothesis testing. In composite hypothesis testing, unlike in simple hypothesis testing, the probability function of the observed data, given the hypothesis, is uncertain as it depends on the unknown value of some parameter. The proposed approach is to minimize the worst case ratio between the probability of error of a decision rule that is independent of the unknown parameters and the minimum probability of error attainable given the parameters. The principal solution to this minimax problem is presented and the resulting decision rule is discussed. Since the exact solution is, in general, hard to find, and a fortiori hard to implement, an approximation method that yields an asymptotically minimax decision rule is proposed. Finally, a variety of potential application areas are provided in signal processing and communications with special emphasis on universal decoding     

Using the matrix pencil method to estimate the parameters of a sumof complex exponentials

The approximation of a function by a sum of complex exponentials is a problem that is at least two centuries old. Fundamentally, all techniques discussed in this article proceed from using the same sequence of data samples and vary only, but importantly, in how those samples are used in achieving the parameter estimation. All of these techniques, in other words, seek the same quantitative parameters to represent the sampled data, but use different routes to get there. The techniques for estimating the parameters are either linear or nonlinear. The linear techniques are emphasized in this presentation. In particular, the matrix pencil method is described, which is more robust to noise in the sampled data. The matrix pencil approach has a lower variance of the estimates of the parameters of interest than a polynomial-type method (Prony's method belongs to this category), and is also computationally more efficient. A bandpass version of the matrix pencil can be implemented in hardware, utilizing an AT&T DSP32C chip operating in real time. A copy of the computer program implementing the matrix pencil technique is given in the appendix     

Numerical solution of the problem of diffraction of electromagnetic waves by nonplanar screens of complex geometric shapes by means of a subhierarchic method

The problem of diffraction of an electromagnetic wave by a nonplanar screen of a complex geometric shape located in free space is considered. The problem is reduced to an integral equation. A numerical method is proposed and realized with the use of rooftop functions for the solution of the integral equation. A subhierarchic method is applied for the solution of the integral equation. Numerical results are presented.     

A practical method for designing FIR digital filters in the complexdomain

A new method is presented for the design of FIR fillers in the complex domain. The method converts the complex approximation problem into an equivalent real nonlinear optimization problem, which is solved by successive linearization using an effective geometrical linearization technique. The method converges rapidly, and the solution has a guaranteed accuracy. It also has the flexibility of allowing addition of extra constraints such as constant group delay constraints and transition-band magnitude overshoot constraints. Numerical examples are presented to illustrate the performance of the method