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<p> EEG is a noninvasive technique useful for the human brain mapping and for the estimation of neural electrical activities in human brain. A goal of processing EEG signals of a subject is the localization of neural current sources in human brain known as dipoles. Although this location estimation problem can be modeled as a particular kind of parameter estimation problem as in array signal processing, the nonlinear structure of an EEG electrode array, which is much more complicated than a traditional sensor array, makes the problem more difficult. </p> <p> In this thesis, we formulate the inverse problem of the forward model on computing the scalp EEG at a finite set of sensors from multiple dipole sources. It is observed that the geometric structure of the EEG array plays a crucial role in ensuring a unique solution for this problem. We first present a necessary and sufficient condition in the model of a single rotating dipole, that guarantees its location to be uniquely determined, when the second-order statistic of the EEG observation is available. In addition, for a single rotating dipole, a closed-form solution to uniquely determine its position is obtained by exploiting the geometrical structure of the EEG array. </p> <p> In the case of multiple dipoles, we suggest the use of the Maximum Likelihood (ML) estimator, which is often considered optimum in parameter estimation. We propose an efficient localization algorithm based on QR decomposition. Depending on whether or not the probability density functions of the dipole amplitude and the noise are available, we utilize the non-coherent ML or the LS as the criterion to develop a unified successive localization algorithm, so that solving the original multi-dipole optimization problem can be approximated by successively solving a series of single-dipole optimization problems. Numerical simulations show that our methods have much smaller estimation errors than the existing RAP-MUSIC method under non-ideal situations such as low SNR with small number of EEG sensors. </p> / Thesis / Master of Applied Science (MASc)

Due to the enormous performance gains associated with the use of antenna arrays in wireless networks, it is inevitable that these technologies will become an integral part of future systems. This report focuses on signal propagation modeling for antenna array systems and on its relationship to the performance of these systems. Accurate simulation and analytical models are prerequisite to the characterization of antenna array system performance. Finally, an understanding of the performance of these systems in various environments is needed for effective overall network design. This report begins with an overview of the fundamentals of antenna array systems. A survey of vector channel models is presented. Angle of arrival and time of arrival statistics for the circular and elliptical (Liberti's Model) models are derived. A generalized optimum output SINR analysis is derived for space-time processing structures in frequency selective fading channels. The hardware and software of the MPRG Antenna Array Testbed (MAAT) is described. A literature review of previous antenna array propagation measurements is given. Antenna array measurement results obtained with the MAAT are used to compare the properties of the received signal vector in the various environmental conditions. The influence of channel parameters on the ability of antenna arrays to separate the signals of two users on the reverse link is studied using simulation. Finally, forward link beamforming techniques are reviewed. / Ph. D.

The proposed demodulator is an all-digital implementation of a FM demodulator. The proposed design intends to implement a FM demodulator for high-speed applications, which makes the requirements for analog components minimal. The proposed circuit is an all-digital quadrature demodulator, where the individual components have been implemented without using any multipliers. The topology uses a Pulse width modulation (PWM) block to avoid the need for a DAC. The Xilinx virtex-7 FPGA has been used as the reference device for the work. The circuit is validated through behavioral simulations and the results conclude the proposed circuit demodulates the targeted FM channel and provides the spectrum information for the targeted FM channel / Master of Science / With the rise in popularity of reconfigurable hardware, such as FPGAs, digital signal processing has become one of the most widespread usage of such devices. The major advantage of using FPGAs for implementing signal processing algorithms is that they provide very less time to market and can be re-modeled or modified in easily. Moreover, the netlists designed for FPGAs can be easily translated to ASICs. As wireless communication has become omnipresent, modulation and demodulation schemes have become an area of great interest. With the increase in data rates for the modern-day communication systems, the digital implementation of these algorithms is becoming more and more common. This is further aided by the advancements in high-speed ADCs and the Electronic Design Automation (EDA) tools, which have made the usage of FPGAs lot more feasible and a lot more efficient. This work discusses the demodulation scheme for one of the most widespread modulation algorithms, Frequency Modulation (FM). An all-digital FM demodulator design is proposed for highspeed implementation on FPGAs. The proposed design is an all-digital quadrature I-Q based demodulator.

Methods of expressing the radiation patterns of phased arrays in closed form that include the effects of radiated mutual coupling are investigated. The two basic methods considered are the classical array analysis method and the active element pattern methods. The theoretical derivations of the active element pattern methods are presented and the various types of active element patterns are defined. Also, a new method based on active element patterns, the hybrid active element pattern method, is introduced which accurately predicts the patterns of small and moderately-sized arrays of equally-spaced elements. Arrays of center-fed dipoles are considered in this study since dipole arrays can be fully characterized, including mutual coupling, using modem numerical electromagnetic analysis codes, thus allowing verification of the array analysis methods presented here. The results are general, however, and may be applied to arrays of any type of element. The array patterns computed using the classical analysis method and the active element pattern methods are compared to those computed using ideal array analysis and the highly-accurate numerical codes. / Master of Science

A bulk of the research on piezoelectric systems in recent years can be classified into two categories, 1) studies of linear piezoelectric oscillator arrays, 2) studies of nonlinear piezoelectric oscillators. This dissertation derives novel linear and nonlinear modeling and estimation methods for such piezoelectric systems. In the first part, this work develops modeling and design methods for Piezoelectric Subordinate Oscillator Arrays (PSOAs) for the wideband vibration attenuation problem. PSOAs offer a straightforward and low mass ratio solution to cancel out the resonant peaks in a host structure's frequency domain. Further, they provide adaptability through shunt tuning, which gives them the ability to recover performance losses because of structural parameter errors. This dissertation studies the derivation of governing equations that result in a closed-form expression for the frequency response function. It also analyzes systematic approaches to assign distributions to the nondimensional parameters in the frequency response function to achieve the desired flat-band frequency response. Finally, the effectiveness of PSOAs under ideal and nonideal conditions are demonstrated in this dissertation through extensive numerical and experimental studies. The concept of performance recovery, introduced in empirical studies, gives a measure of the PSOA's effectiveness in the presence of disorder before and after capacitive tuning. The second part of this dissertation introduces novel modeling and estimation methods for nonlinear piezoelectric oscillators. Traditional modeling techniques require knowledge of the structure as well as the source of nonlinearity. Data-driven modeling techniques used extensively in recent times build approximations. An adaptive estimation method, that uses reproducing kernel Hilbert space (RKHS) embedding methods, can estimate the underlying nonlinear function that governs the system's dynamics. A model built by such a method can overcome some of the limitations of the modeling approaches mentioned above. This dissertation discusses (i) how to construct the RKHS based estimator for the piezoelectric oscillator problem, (ii) how to choose kernel centers for approximating the RKHS, and (iii) derives sufficient conditions for convergence of the function estimate to the actual function. In each of these discussions, numerical studies are used to show the RKHS based adaptive estimator's effectiveness for identifying linearities in piezoelectric oscillators. / Doctor of Philosophy / Piezoelectric materials are materials that generate an electric charge when mechanical stress is applied, and vice versa, in a lossless transformation. Engineers have used piezoelectric materials for a variety of applications, including vibration control and energy harvesting. This dissertation introduces (1) novel methods for vibration attenuation using an array of piezoelectric oscillators, and (2) methods to model and estimate the nonlinear behavior exhibited by piezoelectric materials at very high mechanical forces or electric charges. Arrays of piezoelectric oscillators attached to a host structure are termed piezoelectric subordinate oscillator arrays (PSOAs). With the careful design of PSOAs, we show that we can reduce the vibration of the host structure. This dissertation analyzes methodologies for designing PSOAs and illustrates their vibration attenuation capabilities numerically and experimentally. The numerical and experimental studies also illustrate the robustness of PSOAs. In the second part of this dissertation, we analyze reproducing kernel Hilbert space embedding methods for adaptive estimation of nonlinearities in piezoelectric systems. Kernel methods are extensively used in machine learning, and control theorists have studied adaptive estimation of functions in finite-dimensional spaces. In this work, we adapt kernel methods for adaptive estimation of functions in infinite-dimensional spaces that appear while modeling piezoelectric systems. We derive theorems that ensure convergence of function estimates to the actual function and develop algorithms for careful selection of the kernel basis functions.

In the emerging arena of face-to-face collaboration using large, wall-size screens, a good videoconferencing system would be useful for two locations which both have a large screen. But as screens get bigger, a single camera becomes less than adequate to drive a videoconferencing system for the entire screen. Even if a wide-angle camera is placed in the center of the screen, it's possible for people standing at the sides to be hidden. We can fix this problem by placing several cameras evenly distributed in a grid pattern (what we call a sparse camera array) and merging the photos into one image. With a single camera, people standing near the sides of the screen are viewing an image with a viewpoint at the middle of the screen. Any perspective projection used in this system will look distorted when standing at a different viewpoint. If an orthogonal projection is used, there will be no perspective distortion, and the image will look correct no matter where the viewer stands. As a first step in creating this videoconferencing system, we use stereo matching to find the real world coordinates of objects in the scene, from which an orthogonal projection can be generated. / Master of Science

This thesis addresses the partitioning problem for configurable computing machines. Specifically, this thesis presents algorithms to partition chain-structured task graphs across configurable computing machines. The algorithms give optimal solutions for throughput and total execution time for these problems under constraints on area, pin count, and power consumption. The algorithms provide flexibility for applying these constraints while remaining polynomial in complexity. Proofs of correctness as well as an analysis of runtime complexity are given. Experiments are performed to illustrate the runtime of these algorithms. / Master of Science

FPGAs provide an ideal template for run-time reconfigurable (RTR) designs. Only recently have RTR enabling design tools that bypass the traditional synthesis and bitstream generation process for FPGAs become available. The JBits tool suite is an environment that provides support for RTR designs on Xilinx Virtex and 4K devices. This research provides a comprehensive design process description of a two-dimensional discrete wavelet transform (DWT) core using the JBits run-time reconfigurable FPGA design tool suite. Several aspects of the design process are discussed, including implementation, simulation, debugging, and hardware interfacing to a reconfigurable computing platform. The DWT lends itself to a straightforward implementation in hardware, requiring relatively simple logic for control and address generation circuitry. Through the application of RTR techniques to the DWT, this research attempts to exploit certain advantages that are unobtainable with static implementations. Performance results of the DWT core are presented, including speed of operation, resource consumption, and reconfiguration overhead times. / Master of Science