Tapan K. Sarkar

Bio: Tapan K. Sarkar is an academic researcher from Syracuse University. The author has contributed to research in topics: Integral equation & Antenna (radio). The author has an hindex of 67, co-authored 837 publications receiving 22072 citations. Previous affiliations of Tapan K. Sarkar include University of Belgrade & Technical University of Madrid.

The finite element method in electromagnetics

Abstract: This Key Note presents a summary of the development of the Finite Element Method in the field of Electromagnet ic Engineering, together with a description of several contributions of the authors to the Finite Element Method and its application to the solution of electromagnetic problems. First, a self-adaptive mesh scheme is presented in the context of the quasi-static and full-wave analysis of general anisotropic multiconductor arbitrary shaped waveguiding structures. A comparison between two a posteriori error estimates is done. The first one is based on the complete residual of the differential equations defining the problem. The second one is based on a recovery or smoothing technique of the electromagnetic field. Next, an implementation of the first family of Nedelec's curl-conforming elements done by the authors is outlined. Its features are highlighted and compared with other curl-conforming elements. A presentation of an iterative procedure using a numerically exact radiation condition for the analysis of open (scattering and radiation) problems follows. Other contributions of the authors, like the use of wavelet like basis functions and an implementation of a Time Domain Finite Element Method in the context of two-dimensional scattering problems are only mentioned due to the lack of space.

Matrix pencil method for estimating parameters of exponentially damped/undamped sinusoids in noise

Abstract: A study of a matrix pencil method for estimating frequencies and damping factors of exponentially damped and/or undamped sinusoids in noise is presented. Comparison of this method to a polynomial method (SVD-Prony method) shows that the matrix pencil method and the polynomial method are two special cases of a matrix prediction approach and that the pencil method is more efficient in computation and less restrictive about signal probes. It is found through perturbation analysis and simulation that, for signals with unknown damping factors, the pencil method is less sensitive to noise than the polynomial method. An expression of the Cramer-Rao bound for the exponential signals is presented. >

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

Abstract: 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. >

A survey of various propagation models for mobile communication

Abstract: In order to estimate the signal parameters accurately for mobile systems, it is necessary to estimate a system's propagation characteristics through a medium. Propagation analysis provides a good initial estimate of the signal characteristics. The ability to accurately predict radio-propagation behavior for wireless personal communication systems, such as cellular mobile radio, is becoming crucial to system design. Since site measurements are costly, propagation models have been developed as a suitable, low-cost, and convenient alternative. Channel modeling is required to predict path, loss and to characterize the impulse response of the propagating channel. The path loss is associated with the design of base stations, as this tells us how much a transmitter needs to radiate to service a given region. Channel characterization, on the other hand, deals with the fidelity of the received signals, and has to do with the nature of the waveform received at a receiver. The objective here is to design a suitable receiver that will receive the transmitted signal, distorted due to the multipath and dispersion effects of the channel, and that will decode the transmitted signal. An understanding of the various propagation models can actually address both problems. This paper begins with a review of the information available on the various propagation models for both indoor and outdoor environments. The existing models can be classified into two major classes: statistical models and site-specific models. The main characteristics of the radio channel - such as path loss, fading, and time-delay spread - are discussed. Currently, a third alternative, which includes many new numerical methods, is being introduced to propagation prediction. The advantages and disadvantages of some of these methods are summarized. In addition, an impulse-response characterization for the propagation path is also presented, including models for small-scale fading, Finally, it is shown that when two-way communication ports can be defined for a mobile system, it is possible to use reciprocity to focus the energy along the direction of an intended user without any explicit knowledge of the electromagnetic environment in which the system is operating, or knowledge of the spatial locations of the transmitter and the receiver.

Generalized pencil-of-function method for extracting poles of an EM system from its transient response

Abstract: A generalized pencil-of-function (GPOF) method is developed for extracting the poles of an electromagnetic system from its transient response. The GPOF method needs the solution of a generalized eigenvalue problem to find the poles. Subspace decomposition is also used to optimize the performance of the GPOF method. The GPOF method has advantages over the Prony method in both computation and noise sensitivity, and approaches the Cramer-Rao bound when the signal-to-noise ratio (SNR) is above threshold. An application of the GPOF method to a thin-wire target is presented. >

Spectrum estimation and harmonic analysis

Abstract: In the choice of an estimator for the spectrum of a stationary time series from a finite sample of the process, the problems of bias control and consistency, or "smoothing," are dominant. In this paper we present a new method based on a "local" eigenexpansion to estimate the spectrum in terms of the solution of an integral equation. Computationally this method is equivalent to using the weishted average of a series of direct-spectrum estimates based on orthogonal data windows (discrete prolate spheroidal sequences) to treat both the bias and smoothing problems. Some of the attractive features of this estimate are: there are no arbitrary windows; it is a small sample theory; it is consistent; it provides an analysis-of-variance test for line components; and it has high resolution. We also show relations of this estimate to maximum-likelihood estimates, show that the estimation capacity of the estimate is high, and show applications to coherence and polyspectrum estimates.

Discrete-Dipole Approximation For Scattering Calculations

Abstract: The discrete-dipole approximation (DDA) for scattering calculations, including the relationship between the DDA and other methods, is reviewed. Computational considerations, i.e., the use of complex-conjugate gradient algorithms and fast-Fourier-transform methods, are discussed. We test the accuracy of the DDA by using the DDA to compute scattering and absorption by isolated, homogeneous spheres as well as by targets consisting of two contiguous spheres. It is shown that, for dielectric materials (|m| ≲ 2), the DDA permits calculations of scattering and absorption that are accurate to within a few percent.

The Geometry of Algorithms with Orthogonality Constraints

Abstract: In this paper we develop new Newton and conjugate gradient algorithms on the Grassmann and Stiefel manifolds. These manifolds represent the constraints that arise in such areas as the symmetric eigenvalue problem, nonlinear eigenvalue problems, electronic structures computations, and signal processing. In addition to the new algorithms, we show how the geometrical framework gives penetrating new insights allowing us to create, understand, and compare algorithms. The theory proposed here provides a taxonomy for numerical linear algebra algorithms that provide a top level mathematical view of previously unrelated algorithms. It is our hope that developers of new algorithms and perturbation theories will benefit from the theory, methods, and examples in this paper.

Spectral analysis of signals

Abstract: 1. Basic Concepts. 2. Nonparametric Methods. 3. Parametric Methods for Rational Spectra. 4. Parametric Methods for Line Spectra. 5. Filter Bank Methods. 6. Spatial Methods. Appendix A: Linear Algebra and Matrix Analysis Tools. Appendix B: Cramer-Rao Bound Tools. Appendix C: Model Order Selection Tools. Appendix D: Answers to Selected Exercises. Bibliography. References Grouped by Subject. Subject Index.

Meep: A flexible free-software package for electromagnetic simulations by the FDTD method

Abstract: This paper describes Meep, a popular free implementation of the finite-difference time-domain (FDTD) method for simulating electromagnetism. In particular, we focus on aspects of implementing a full-featured FDTD package that go beyond standard textbook descriptions of the algorithm, or ways in which Meep differs from typical FDTD implementations. These include pervasive interpolation and accurate modeling of subpixel features, advanced signal processing, support for nonlinear materials via Pade approximants, and flexible scripting capabilities.