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Research Doctorate - Doctor of Philosophy (PhD) / This thesis studies control systems with communication constraints. Such constraints arise due to the fact that practical control systems often use non-transparent communication links, i.e., links subject to data-rate constraints, random data-dropouts or random delays. Traditional control theory cannot deal with such constraints and the need for new tools and insights arises. We study two problems: control with average data-rate constraints and control over analog erasure channels with i.i.d. dropout profiles. When focusing on average data-rate constraints, it is natural to ask whether information theoretic ideas may assist the study of networked control systems. In this thesis we show that it is possible to use fundamental information theoretic concepts to arrive at a framework that allows one to tackle performance related control problems. In doing so, we show that there exists an exact link between control systems subject to average data-rate limits, and control systems which are closed over additive i.i.d. noise channels subject to a signal-to-noise ratio constraint. On the other hand, in the case of control systems subject to i.i.d. data-dropouts, we show that there exists a second-order moments equivalence between a linear feedback system which is interconnected over an analog erasure channel, and the same system when it is interconnected over an additive i.i.d. noise channel subject to a signal-to-noise ratio constraint. From the results foreshadowed above, it follows that the study of control systems closed over signal-to-noise ratio constrained additive i.i.d. noise channels is a task of relevance to many networked control problems. Moreover, the interplay between signal-to-noise ratio constraints and control objectives is an interesting issue in its own right. This thesis starts with such a study. Then, we use the resultant insights to address performance issues in control systems subject to either average data-rate constraints or i.i.d. data-dropouts. Our approach shows that, once key equivalences are exposed, standard control intuition and synthesis machinery can be used to tackle networked control problems in an exact manner. It also sheds light into fundamental results in the literature and gives (partial) answers to several previously open questions. We believe that the insights in this thesis are of fundamental importance and, to the best of the author's knowledge, novel.

Much of the current research in magnetic resonance engineering focuses on reducing the acquisition time for obtaining an image while simultaneously maximizing the Signal to Noise ratio (SNR) of the image. It is known that improvement in imaging time or resolution is obtained at the cost of SNR. Therefore wherever possible, RF coil engineers design the coil in such a manner so as to maximize SNR for that coil design. In one such design consideration, most coil designers prefer placing low impedance preamplifiers near the coil. The further the pre-amplifiers are from the coil, the greater will be the signal loss due to transmission and higher will be its input impedance as perceived at the coil which would degrade inter-coil isolation. Owing to the current trend of using increasing number of receiver channels (32, 64 or 128) for parallel imaging, placing the preamplifiers near the coil would greatly complicate the coil construction. The primary objective of this research was to find the relation between SNR and referred preamp impedance and whether preamps need to be placed on the coil, or if they can be placed outside the magnet at the end of a transmission line which would simplify the construction of large count array. In addition, SNR was studied as a function of coil design parameters - coil loading, array coil separation, and system frequency. Both theoretical and experimental methods were used to undertake this investigation. A popular electromagnetic modeling technique, finite difference time domain (FDTD), was used to model SNR in arrays of two 3 inch loop coils at 3T and 1.5T. Results were also verified through bench measurement at 3T and 1.5T and by evaluating SNR. To verify the robustness of our results and to assess the possibility of using low cost standard 50 ohm preamps, we carried out additional bench measurements at 4.7T. Results demonstrated that preamplifier placement is critical at low field strength. At higher field strength, SNR degradation due to preamplifier placement was less owing to heavier coil loading.

Obtaining higher depth of imaging is an important goal in Optical Coherence Tomography (OCT) systems. One of the main factors that affect the depth of OCT imaging is the presence of noise. That’s why the study of noise statistics is an important problem. In the first part of this thesis we obtain an empirical estimate of the second order statistics of noise by using a sequence of Time domain (TD) OCT images. These estimates confirm the non-stationary nature of noise in TD-OCT. In the second part of the thesis these estimates are used to design a depth-dependent matched filter to maximize the Signal-to-Noise Ratio (SNR) and increase the Contrast-to-Noise Ratio (CNR) in TD-OCT. By applying our filter to TD-OCT images of both vascular rabbit tissue and a human tooth, both SNR and CNR were increased and a higher imaging depth was achieved.

Obtaining higher depth of imaging is an important goal in Optical Coherence Tomography (OCT) systems. One of the main factors that affect the depth of OCT imaging is the presence of noise. That’s why the study of noise statistics is an important problem. In the first part of this thesis we obtain an empirical estimate of the second order statistics of noise by using a sequence of Time domain (TD) OCT images. These estimates confirm the non-stationary nature of noise in TD-OCT. In the second part of the thesis these estimates are used to design a depth-dependent matched filter to maximize the Signal-to-Noise Ratio (SNR) and increase the Contrast-to-Noise Ratio (CNR) in TD-OCT. By applying our filter to TD-OCT images of both vascular rabbit tissue and a human tooth, both SNR and CNR were increased and a higher imaging depth was achieved.

Research Doctorate - Doctor of Philosophy (PhD) / This thesis studies control systems with communication constraints. Such constraints arise due to the fact that practical control systems often use non-transparent communication links, i.e., links subject to data-rate constraints, random data-dropouts or random delays. Traditional control theory cannot deal with such constraints and the need for new tools and insights arises. We study two problems: control with average data-rate constraints and control over analog erasure channels with i.i.d. dropout profiles. When focusing on average data-rate constraints, it is natural to ask whether information theoretic ideas may assist the study of networked control systems. In this thesis we show that it is possible to use fundamental information theoretic concepts to arrive at a framework that allows one to tackle performance related control problems. In doing so, we show that there exists an exact link between control systems subject to average data-rate limits, and control systems which are closed over additive i.i.d. noise channels subject to a signal-to-noise ratio constraint. On the other hand, in the case of control systems subject to i.i.d. data-dropouts, we show that there exists a second-order moments equivalence between a linear feedback system which is interconnected over an analog erasure channel, and the same system when it is interconnected over an additive i.i.d. noise channel subject to a signal-to-noise ratio constraint. From the results foreshadowed above, it follows that the study of control systems closed over signal-to-noise ratio constrained additive i.i.d. noise channels is a task of relevance to many networked control problems. Moreover, the interplay between signal-to-noise ratio constraints and control objectives is an interesting issue in its own right. This thesis starts with such a study. Then, we use the resultant insights to address performance issues in control systems subject to either average data-rate constraints or i.i.d. data-dropouts. Our approach shows that, once key equivalences are exposed, standard control intuition and synthesis machinery can be used to tackle networked control problems in an exact manner. It also sheds light into fundamental results in the literature and gives (partial) answers to several previously open questions. We believe that the insights in this thesis are of fundamental importance and, to the best of the author's knowledge, novel.

Thesis advisor: John E. Ebel / Determination of the source parameters of a local earthquake from full seismic waveforms requires seismograms with clear body-wave signals from the earthquake source. Coherence of the earthquake body-wave seismograms recorded at two different receivers can be used to estimate the signal-to-noise ratio (SNR) of the body-wave energy radiated by the source. In this study, the coherence of earthquake body waves recorded in the Northeastern United States and Southeastern Canada (NEUSSEC) is measured as a function of frequency, interstation distance, and ambient SNR, and then used as an estimate of body-wave SNR. Seismograms from the CN, IU, LD, N4, NE, TA, and US arrays were used to measure coherence between stations with a mean separation of 70 km. Seismograms from the Acton Littleton Seismic Array (ALSA) were used to measure coherence at 5 km mean station separation. Coherence is measured at frequencies between 0.05-10 Hz for Pn and Sn phases from NEUSSEC earthquakes with magnitudes (M) between 0.0 and 4.7 at epicentral distances between 180-1800 km as well as at frequencies between 0.05-10 Hz for the first arrivals of P and S waves from earthquakes M>6 at distances >2500 km. The teleseismic P waves display values of coherence greater than 0.9 out to interstation distances of 1500 km at frequencies <0.8 Hz, but as frequency increases, the interstation distance at which coherence falls below 0.9 decreases. Teleseismic S and regional Pn and Sn waves display coherence values around 0.5, suggesting the amplitudes of the body-waves are smaller than those of the noise, which likely is the result of converted and reflected or refracted P waves and/or smaller signal amplitudes. These coherence values are compared to the coherence values of ambient noise. For any two P, S, Pn or Sn waveforms recorded in the NEUSSEC at 3-5 Hz there is a 50% or greater chance of those two waveforms containing coherent energy that is not ambient noise; these frequencies are where this percent chance is greatest for all seismic phases. At frequencies between 3-5 Hz the effects of scattering are most pronounced on the coherence values of regional seismic phases, suggesting that most scattering in the crust of the NEUSSEC takes place at these frequencies. Teleseismic seismic phases do not include as much scattered energy as the regional seismic phases at 3-5 Hz, and must therefore encounter fewer scattering heterogeneities along their travel path than the regional seismic phases. / Thesis (MS) — Boston College, 2021. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Earth and Environmental Sciences.

In system identification, different methods are often classified as parametric or non-parametric methods. For parametric methods, a parametric model of a system is considered and the model parameters are estimated. For non-parametric methods, no parametric model is used and the result of the identification is given as a curve or a function. One of the non-parametric methods is the impulse response analysis. This approach is dynamic simulation. This thesis introduces a new paradigm for dynamic simulation, called impulse-based simulation. This approach is based on choosing a Dirac function as input, and as a result, the output will be equal to the impulse response. However, a Dirac function cannot be realized in practice, and an approximation has to be used. As a consequence, the output will deviate from the impulse response. Once the impulse response is estimated, a parametric model can be fitted to the estimation. This thesis aims to determine the parameters in a parametric model from an estimated impulse response. The process of investigating the models is a critical aspect of the project. Correlation analysis is used to obtain the weighting function from the estimates of covariance functions. Later, a relation formed between the parameters and the estimates (obtained by correlation analysis) in the form of a linear system of equations. Furthermore, simulations are carried out using Monte Carlo for investigating the properties of the two step approach, which involves in correlation analysis to find h-parameters and least squares and total least squares methods to solve for the parameters of the model. In order to evaluate the complete capability of the approach to the noise variation a study of signal to noise ratio and mean, mean square error and variances of the estimated parameters is carried out. The results of the Monte Carlo study indicate that two-step approach can give rather accurate parameter estimates. In addition, the least squares and total least squares methods give similar results.