I address the geometric problem of the pendulum-like swinging of towed birds for AEM platforms. I establish a link between actual observed bird swing and its effect on survey data for two different systems and explain the link by a model that compares actual survey data to the calculated mutual inductance coupling of a dipole pair over an infinitely conductive half space, which pair is permitted arbitrary pitch, roll and altitude changes. I develop a non-linear filter that removes bird swing effects from survey data which successfully corrected data from 3 different AEM surveys. Calibration of several different time domain AEM systems is attempted using an accurately laid out and surveyed, closed, multi-turn loop of known resistance and self-inductance that is placed on - but insulated from - resistive ground. I derive a rigourous mathematical model that predicts airborne receiver's response to the coupling to the transmitter current waveform and total system geometry. The method was proven to be successful over resistive ground, with significant system problems identified such as: altimetry error, spatial averaging of data during postprocessing, error in the predicted horizontal position of the AEM platform, receiver windowing and timing errors and bird swing. I show that, although we can calibrate a time domain AEM system for a single flyover, it is impossible to calibrate an AEM system for geometry. As an intermediate step in the calibration process, I show that by monitoring the current induced in the ground loop we can obtain the waveform of the AEM transmitter current throu gh deconvolution in the Fourier domain. Simple and cost effective methods for the improvement of quantitative AEM data are presented in this thesis. However, until the geometry problem of AEM platforms is solved, full system calibration will not be obtained and filters will need to be applied to the data. I recommend the use of: GPS antennas mounted on all towed birds, able to be post-processed for accurate position recovery, reliable bird-mounted scanning altimeters that do not rely on range-finding technology but instead employ a shortest path algorithm, pitch and roll sensors mounted on the trailed bird and the measurement of airspeed of both the towed bird and the aircraft during surveys.

Herein we present the development of a fluorescence-enhanced, frequency-domain radiative transport reconstruction system designed for small animal optical tomography. The system includes a time-dependent data acquisition instrument, a radiative transport based forward model for prediction of time-dependent propagation of photons in small, non-diffuse volumes, and an algorithm which utilizes the forward model to reconstruct fluorescent yields from air/tissue boundary measurements. The major components of the instrumentation include a charge coupled device camera, an image intensifier, signal generators, and an optical switch. Time-dependent data were obtained in the frequency-domain using homodyne techniques on phantoms with 0.2% to 3% intralipid solutions. Through collaboration with Transpire, Inc., a fluorescence-enhanced, frequency-domain, radiative transport equation (RTE) solver was developed. This solver incorporates the discrete ordinates, source iteration with diffusion synthetic acceleration, and linear discontinuous finite element differencing schemes, to predict accurately the fluence of excitation and emission photons in diffuse and transport limited systems. Additional techniques such as the first scattered distributed source method and integral transport theory are used to model the numerical apertures of fiber optic sources and detectors. The accuracy of the RTE solver was validated against diffusion and Monte Carlo predictions and experimental data. The comparisons were favorable in both the diffusion and transport limits, with average errors of the RTE predictions, as compared to experimental data, typically being less than 8% in amplitude and 7% in phase. These average errors are similar to those of the Monte Carlo and diffusion predictions. Synthetic data from a virtual mouse were used to demonstrate the feasibility of using the RTE solver for reconstructing fluorescent heterogeneities in small, non-diffuse volumes. The current version of the RTE solver limits the reconstruction to one iteration and the reconstruction of marginally diffuse, frequency-domain experimental data using RTE was not successful. Multiple iterations using a diffusion solver successfully reconstructed the fluorescent heterogeneities, indicating that, when available, multiple iterations of the RTE based solver should also reconstruct the heterogeneities.

The thesis treats model reduction for linear time-varying systems. Time-varying models appear in many fields, including power systems, chemical engineering, aeronautics, and computational science. They can also be used for approximation of time-invariant nonlinear models. Model reduction is a topic that deals with simplification of complex models. This is important since it facilitates analysis and synthesis of controllers. The thesis consists of two parts. The first part provides an introduction to the topics of time-varying systems and model reduction. Here, notation, standard results, examples, and some results from the second part of the thesis are presented. The second part of the thesis consists of four papers. In the first paper, we study the balanced truncation method for linear time-varying state-space models. We derive error bounds for the simplified models. These bounds are generalizations of well-known time-invariant results, derived with other methods. In the second paper, we apply balanced truncation to a high-order model of a diesel exhaust catalyst. Furthermore, we discuss practical issues of balanced truncation and approximative discretization. In the third paper, we look at frequency-domain analysis of linear time-periodic impulse-response models. By decomposing the models into Taylor and Fourier series, we can analyze convergence properties of different truncated representations. In the fourth paper, we use the frequency-domain representation developed in the third paper, the harmonic transfer function, to generalize Bode's sensitivity integral. This result quantifies limitations for feedback control of linear time-periodic systems. / QC 20120206

The application of photoacoustic (PA) phenomena to medical imaging has been investigated for more than a decade. To implement this modality, one may choose between two types of laser sources, pulsed or continuous wave (CW). This selection affects all features of the imaging technique. Nowadays pulsed lasers are the state-of-the-art technique in the PA research. In this work, various features of the alternative frequency-domain (FD) PA were investigated. An axially symmetric transfer function model of PA wave generation and a Krimholtz-Leedom-Matthaei (KLM) transducer model were developed and used to analyze the experimental results. The controllable parameters of the FD-PA were optimized to improve the signal-to-noise ratio (SNR), contrast, axial resolution and depth detectivity. For example, it was shown that employing the optimal chirp bandwidth can enhance the SNR by more than 10 dB. In addition to the image produced by the cross-correlation amplitude, the phase of the correlation signal was used as a separate channel. A statistical method was introduced to generate an image from this phase channel, and also to filter the PA amplitude channel. A study was also performed to compare FD PA and the prevalent pulsed method. Various features of both methods were examined experimentally using a dual-mode PA system and under the condition of maximum permissible exposure (MPE). The SNRs of both methods were evaluated theoretically and experimentally. It was shown that at low frequencies, both modalities generate comparable SNRs, and at high frequencies pulsed PA produces superior SNRs and depth detetivity. However, by increasing the laser power and decreasing the chirp duration within the safety limits, the SNR and depth detectivity of the FD-PA method are enhanced considerably. The main cause to achieve lower experimental SNRs than theoretical predictions for pulsed PA response was shown to be the oscillating baseline, which can be partially eliminated by filtering.

The application of photoacoustic (PA) phenomena to medical imaging has been investigated for more than a decade. To implement this modality, one may choose between two types of laser sources, pulsed or continuous wave (CW). This selection affects all features of the imaging technique. Nowadays pulsed lasers are the state-of-the-art technique in the PA research. In this work, various features of the alternative frequency-domain (FD) PA were investigated. An axially symmetric transfer function model of PA wave generation and a Krimholtz-Leedom-Matthaei (KLM) transducer model were developed and used to analyze the experimental results. The controllable parameters of the FD-PA were optimized to improve the signal-to-noise ratio (SNR), contrast, axial resolution and depth detectivity. For example, it was shown that employing the optimal chirp bandwidth can enhance the SNR by more than 10 dB. In addition to the image produced by the cross-correlation amplitude, the phase of the correlation signal was used as a separate channel. A statistical method was introduced to generate an image from this phase channel, and also to filter the PA amplitude channel. A study was also performed to compare FD PA and the prevalent pulsed method. Various features of both methods were examined experimentally using a dual-mode PA system and under the condition of maximum permissible exposure (MPE). The SNRs of both methods were evaluated theoretically and experimentally. It was shown that at low frequencies, both modalities generate comparable SNRs, and at high frequencies pulsed PA produces superior SNRs and depth detetivity. However, by increasing the laser power and decreasing the chirp duration within the safety limits, the SNR and depth detectivity of the FD-PA method are enhanced considerably. The main cause to achieve lower experimental SNRs than theoretical predictions for pulsed PA response was shown to be the oscillating baseline, which can be partially eliminated by filtering.

This thesis explores and implements techniques for frequency domain modelling and time domain simulation of overhead transmission lines. The popular Vector Fitting algorithm is employed to approximate the frequency domain model using rational functions, and the recursive convolution technique is applied to the rational approximation to generate a time domain form. The frequency domain model is translated into the time domain using delay extraction, modal decomposition, passivity enforcement, and rational approximation. Several approaches to each of these procedures are investigated. The thesis also discusses several choices for the integration method used within the recursive convolution procedure. In order to make the transmission line modeller and simulator easy to use, a Java-based library and partial graphical interface were developed. Specifically, the goal was to develop a platform-independent program that can run either stand-alone or as an applet inside a web page. / October 2005

The problem of modeling systems from frequency response measurements is of interest to many engineers. In electronics, we wish to construct a macromodel from tabulated impedance, admittance or scattering parameters to incorporate it into a circuit simulator for performing circuit analyses. Structural engineers employ frequency response functions to determine the natural frequencies and damping coefficients of the underlying structure. Subspace identification, popular among control engineers, and vector fitting, used by electronics engineers, are examples of algorithms developed for this problem. This thesis has three goals. 1. For multi-port devices, currently available algorithms arc expensive. This thesis therefore proposes an approach based on the Loewner matrix pencil constructed in the context of tangential interpolation with several possible implementations. They are fast, accurate, build low dimensional models, and are especially designed for a large number of terminals. For noise-free data, they identify the underlying system, rather than merely fitting the measurements. For noisy data, their performance is analyzed for different noise levels introduced in the measurements and an improved version, which identifies an approximation of the original system even for large noise values, is proposed. 2. This thesis addresses the problem of generating parametric models from measurements performed with respect to the frequency, but also with respect to one or more design parameters, which could relate to geometry or material properties. These models are suited for performing optimization over the design variables. The proposed approach generalizes the Loewner matrix to data depending on two variables. 3. This thesis analyzes the convergence properties of vector fitting, an iterative algorithm that relocates the poles of the model, given some "starting poles" chosen heuristically. It was recognized as a reformulation of the Sanathanan-Koerner iteration and several authors attempted to improve its convergence properties, but a thorough convergence analysis has been missing. Numerical examples show that for high signal to noise ratios, the iteration is convergent, while for low ones, it may diverge. Hence, incorporating a Newton step aims at making the iteration always convergent for "starting poles" chosen close to the solution. A connection between vector fitting and the Loewner framework is exhibited, which resolves the issue of choosing the starting poles.

Herein we present the development of a fluorescence-enhanced, frequency-domain radiative transport reconstruction system designed for small animal optical tomography. The system includes a time-dependent data acquisition instrument, a radiative transport based forward model for prediction of time-dependent propagation of photons in small, non-diffuse volumes, and an algorithm which utilizes the forward model to reconstruct fluorescent yields from air/tissue boundary measurements. The major components of the instrumentation include a charge coupled device camera, an image intensifier, signal generators, and an optical switch. Time-dependent data were obtained in the frequency-domain using homodyne techniques on phantoms with 0.2% to 3% intralipid solutions. Through collaboration with Transpire, Inc., a fluorescence-enhanced, frequency-domain, radiative transport equation (RTE) solver was developed. This solver incorporates the discrete ordinates, source iteration with diffusion synthetic acceleration, and linear discontinuous finite element differencing schemes, to predict accurately the fluence of excitation and emission photons in diffuse and transport limited systems. Additional techniques such as the first scattered distributed source method and integral transport theory are used to model the numerical apertures of fiber optic sources and detectors. The accuracy of the RTE solver was validated against diffusion and Monte Carlo predictions and experimental data. The comparisons were favorable in both the diffusion and transport limits, with average errors of the RTE predictions, as compared to experimental data, typically being less than 8% in amplitude and 7% in phase. These average errors are similar to those of the Monte Carlo and diffusion predictions. Synthetic data from a virtual mouse were used to demonstrate the feasibility of using the RTE solver for reconstructing fluorescent heterogeneities in small, non-diffuse volumes. The current version of the RTE solver limits the reconstruction to one iteration and the reconstruction of marginally diffuse, frequency-domain experimental data using RTE was not successful. Multiple iterations using a diffusion solver successfully reconstructed the fluorescent heterogeneities, indicating that, when available, multiple iterations of the RTE based solver should also reconstruct the heterogeneities.

Many empirical studies show that both equity volatility and its trading volume have long range dependence and can be modeled as fractional integrated processes. The objective of this study is to investigate relationship between volatility and volume.We adopt four estimators of volatility, which includes the squared log returns, historical volatility, iterative t estimators and $GARCH$ estimators. The results show that among the four estimators squared log returns usually have the largest integration orders and produce hightest ratios of fractional cointegration. The fractional integrated orders are estimated separately and jointly, and the cointegration parameters are estimated by ordinary least squares, a narrow band frequency domain least squares method and a semiparametric estimator of Whittle likelihood. Models are also established when volatility and volume are not fractional cointegrated.

This study, explores the use of an iterative solution approach for the linearized Euler equations formulated in the frequency domain for fan tone noise propagation and radiation through bypass jets. The aim is to be able to simulate high frequency propagation and radiation phenomena with this code, without excessive computational resources. All computations are performed in parallel using MPI library routines on a computer cluster. The linearized Euler equations support the Kelvin-Helmholtz type convective physical instabilities in jet shear flows. If these equations are solved directly in frequency domain, the unstable modes may be filtered out for the frequencies of interest. However, direct solutions are memory intensive and the reachable frequency is limited. Results provided shown that iterative solution of LEE is more efficient when considered memory requirement and might solve a wider scope of frequencies, if the instabilities are controlled.