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The objective of the proposed research is to develop simplified reconfigurable transmission systems with frequency multipliers for the transmission of complex modulated signals. Because they rely on nonlinear properties, frequency multiplier-based transmission systems require proper linearization techniques and accurate modeling of the signal transfer function. To accomplish these two goals, the author has developed techniques to model and linearize frequency multipliers and to digitize feedback signals for nonlinear characterization. First, adaptive predistortion techniques and zonal transfer theories have been developed for modeling and linearization. The predistortion system has been verified by applying an IS-95B signal to various frequency multipliers built by the author. Second, because the output signals at higher harmonic zones occupy wider frequency bandwidths than the signal in the fundamental zone does and thus make it harder to use traditional sampling techniques, a simplified but effective method called the sub-Nyquist sampling rate was developed and verified. Third, two methods for reconfigurable transmitters using frequency multipliers in conjunction with digital predistortion linearizers were developed. Both methods make it possible to transmit complex signals via frequency multipliers by using dual-band transmission systems that incorporate frequency multipliers that are based on linearization techniques. One of these methods uses a circuit topology that can be switched between a fundamental-mode in-phase combined amplifier and a push-push frequency doubler using input phasing. The second suggested method uses a fundamental-frequency power amplifier followed by a varactor multiplier that can be bypassed with an RF switch. This work will contribute to the development of low-cost and size-effective reconfigurable transmission systems because it requires fewer transmitting components and needs less sampling of the feedback networks.

Cost reduction has been and will continue to be a primary driving force in the evolution of hardware design and associated technologies. The objective of this research is to design low-cost signal acquisition systems for characterizing wideband and high-speed signals. As the bandwidth and the speed of such signals increase, the cost of testing also increases significantly; therefore, innovative hardware and algorithm co-design are needed to relieve this problem. In Chapter 2, a low-cost multi-rate system is proposed for characterizing the spectra of wideband signals. The design is low-cost in the sense of the actual component cost, the system complexity, and the effort required for calibration. The associated algorithms are designed such that the hardware can be implemented with low-complexity yet be robust enough to deal with various hardware variations. A hardware prototype is built not only to verify the proposed hardware scheme and algorithms but to serve as a concrete example that shows that characterizing signals with sub-Nyqusit sampling rate is feasible. Chapter 3 introduces a low-cost time-domain waveform reconstruction technique, which requires no mutual synchronization mechanisms. This brings down cost significantly and enables the implementation of systems capable of capturing tens of Gigahertz (GHz) signals for significantly lower cost than high-end oscilloscopes found in the market today. For the first time, band-interleaving and incoherent undersampling techniques are combined to form a low-cost solution for waveform reconstruction. This is enabled by co-designing the hardware and the back-end signal processing algorithms to compensate for the lack of coherent Nyquist rate sampling hardware. A hardware prototype was built to support this work. Chapter 4 describes a novel test methodology that significantly reduces the required time for crosstalk jitter characterization in parallel channels. This is done by using bit patterns with coprime periods as channel stimuli and using signal processing algorithms to separate multiple crosstalk coupling effects. This proposed test methodology can be applied seamlessly in conjunction with the current test methodology without re-designing the test setup. More importantly, the conclusion derived from the mathematical analysis shows that only such test stimuli give unbiased characterization results, which are critical in all high-precision test setups. Hardware measurement results and analysis are provided to support this methodology. This thesis starts with an overview of the background and a literature review. Three major previously mentioned works are addressed in three separate chapters. Each chapter documents the hardware designs, signal processing algorithms, and associated mathematical analyses. For the purpose of verification, the hardware measurement setups and results are discussed at the end of these three chapters. The last chapter presents conclusions and future directions for work from this thesis.

The Shannon sampling framework is widely used for discrete representation of analog bandlimited signals, starting from samples taken at the Nyquist rate. In many practical applications, signals are not bandlimited. In order to accommodate such signals within the Shannon-Nyquist framework, one typically passes the signal through an anti-aliasing filter, which essentially performs bandlimiting. In applications such as RADAR, SONAR, ultrasound imaging, optical coherence to-mography, multiband signal communication, wideband spectrum sensing, etc., the signals to be sampled have a certain structure, which could manifest in one of the following forms: (i) sparsity or parsimony in a certain bases; (ii) shift-invariant representation; (iii) multi-band spectrum; (iv) finite rate of innovation property, etc.. By using such structure as a prior, one could devise efficient sampling strategies that operate at sub-Nyquist rates. In this Ph.D. thesis, we consider the problem of sampling and reconstruction of finite-rate-of-innovation (FRI) signals, which fall in one of the two classes: (i) Sum-of-weighted and time-shifted (SWTS) pulses; and (ii) Sum-of-weighted exponential (SWE). Finite-rate-of-innovation signals are not necessarily bandlimited, but they are specified by a finite number of free parameters per unit time interval. Hence, the FRI reconstruction problem could be solved by estimating the parameters starting from measurements on the signal. Typically, parameter estimation is done using high-resolution spectral estimation (HRSE) techniques such as the annihilating filter, matrix pencil method, estimation of signal parameter via rotational invariance technique (ESPRIT), etc.. The sampling issues include design of the sampling kernel and choice of the sampling grid structure. Following a frequency-domain reconstruction approach, we propose a novel technique to design compactly supported sampling kernels. The key idea is to cancel aliasing at certain set of uniformly spaced frequencies and make sure that the rest of the frequency response is specified such that the kernel follows the Paley-Wiener criterion for compactly supported functions. To assess the robustness in the presence of noise, we consider a particular class of the proposed kernel whose impulse response has the form of sum of modulated splines (SMS). In the presence of continuous-time and digital noise cases, we show that the reconstruction accuracy is improved by 5 to 25 dB by using the SMS kernel compared with the state-of-the-art compactly supported kernels. Apart from noise robustness, the SMS kernel also has polynomial-exponential reproducing property where the exponents are harmonically related. An interesting feature of the SMS kernel, in contrast with E-splines, is that its support is independent of the number of exponentials. In a typical SWTS signal reconstruction mechanism, first, the SWTS signal is trans formed to a SWE signal followed by uniform sampling, and then discrete-domain annihilation is applied for parameter estimation. In this thesis, we develop a continuous-time annihilation approach using the shift operator for estimating the parameters of SWE signals. Instead of using uniform sampling-based HRSE techniques, operator-based annihilation allows us to estimate parameters from structured non-uniform samples (SNS), and gives more accurate parameters estimates. On the application front, we first consider the problem of curve fitting and curve completion, specifically, ellipse fitting to uniform or non-uniform samples. In general, the ellipse fitting problem is solved by minimizing distance metrics such as the algebraic distance, geometric distance, etc.. It is known that when the samples are measured from an incomplete ellipse, such fitting techniques tend to estimate biased ellipse parameters and the estimated ellipses are relatively smaller than the ground truth. By taking into account the FRI property of an ellipse, we show how accurate ellipse fitting can be performed even to data measured from a partial ellipse. Our fitting technique first estimates the underlying sampling rate using annihilating filter and then carries out least-squares regression to estimate the ellipse parameters. The estimated ellipses have lesser bias compared with the state-of-the-art methods and the mean-squared error is lesser by about 2 to 10 dB. We show applications of ellipse fitting in iris images starting from partial edge contours. We found that the proposed method is able to localize iris/pupil more accurately compared with conventional methods. In a related application, we demonstrate curve completion to partial ellipses drawn on a touch-screen tablet. We also applied the FRI principle to imaging applications such as frequency-domain optical-coherence tomography (FDOCT) and nuclear magnetic resonance (NMR) spectroscopy. In these applications, the resolution is limited by the uncertainty principle, which, in turn, is limited by the number of measurements. By establishing the FRI property of the measurements, we show that one could attain super-resolved tomograms and NMR spectra by using the same or lesser number of samples compared with the classical Fourier-based techniques. In the case of FDOCT, by assuming a piecewise-constant refractive index of the specimen, we show that the measurements have SWE form. We show how super-resolved tomograms could be achieved using SNS-based reconstruction technique. To demonstrate clinical relevance, we consider FDOCT measurements obtained from the retinal pigment epithelium (RPE) and photoreceptor inner/outer segments (IS/OS) of the retina. We show that the proposed method is able to resolve the RPE and IS/OS layers by using only 40% of the available samples. In the context of NMR spectroscopy, the measured signal or free induction decay (FID) can be modelled as a SWE signal. Due to the exponential decay, the FIDs are non-stationary. Hence, one cannot directly apply autocorrelation-based methods such as ESPRIT. We develop DEESPRIT, a counterpart of ESPRIT for decaying exponentials. We consider FID measurements taken from amino acid mixture and show that the proposed method is able to resolve two closely spaced frequencies by using only 40% of the measurements. In summary, this thesis focuses on various aspects of sub-Nyquist sampling and demonstrates concrete applications to super-resolution imaging.

Electrical bioimpedance spectroscopy (EBIS) has been used to assess the status or composition of various types of tissue, and examples of EBIS include body composition analysis (BCA) and tissue characterisation for skin cancer detection. EBIS is a non-invasive method that has the potential to provide a large amount of information for diagnosis or monitoring purposes, such as the monitoring of pulmonary oedema, i.e., fluid accumulation in the lungs. However, in many cases, systems based on EBIS have not become generally accepted in clinical practice. Possible reasons behind the low acceptance of EBIS could involve inaccurate models; artefacts, such as those from movements; measurement errors; and estimation errors. Previous thoracic EBIS measurements aimed at pulmonary oedema have shown some uncertainties in their results, making it difficult to produce trustworthy monitoring methods. The current research hypothesis was that these uncertainties mostly originate from estimation errors. In particular, time-varying behaviours of the thorax, e.g., respiratory and cardiac activity, can cause estimation errors, which make it tricky to detect the slowly varying behaviour of this system, i.e., pulmonary oedema. The aim of this thesis is to investigate potential sources of estimation error in transthoracic impedance spectroscopy (TIS) for pulmonary oedema detection and to propose methods to prevent or compensate for these errors.   This work is mainly focused on two aspects of impedance spectrum estimation: first, the problems associated with the delay between estimations of spectrum samples in the frequency-sweep technique and second, the influence of undersampling (a result of impedance estimation times) when estimating an EBIS spectrum. The delay between frequency sweeps can produce huge errors when analysing EBIS spectra, but its effect decreases with averaging or low-pass filtering, which is a common and simple method for monitoring the time-invariant behaviour of a system. The results show the importance of the undersampling effect as the main estimation error that can cause uncertainty in TIS measurements.  The best time for dealing with this error is during the design process, when the system can be designed to avoid this error or with the possibility to compensate for the error during analysis. A case study of monitoring pulmonary oedema is used to assess the effect of these two estimation errors. However, the results can be generalised to any case for identifying the slowly varying behaviour of physiological systems that also display higher frequency variations.  Finally, some suggestions for designing an EBIS measurement system and analysis methods to avoid or compensate for these estimation errors are discussed. / <p>QC 20140604</p>

One way of reducing the examination time in magnetic resonance imaging (MRI) is to reduce the amount of raw data acquired, by performing so-called undersampling. Conventionally, MRI data is acquired line-by-line on a Cartesian grid. In the field of Cardiovascular Magnetic Resonance (CMR), however, radial k-space sampling is seen as a promising emerging technique for rapid image acquisitions, mainly due to its robustness against motion disturbances occurring from the beating heart. Whereas Cartesian undersampling will result in image aliasing, radial undersampling will introduce streak artifacts. The objective of this work was to train the deep learning architecture, CycleGAN, to reduce streak artifacts in radially undersampled CMR images, and to evaluate the model performance. A benefit of using CycleGAN over other deep learning techniques for this application is that it can be trained on unpaired data. In this work, CycleGAN network was trained on 3060 radial and 2775 Cartesian unpaired CMR images acquired in human subjects to learn a mapping between the two image domains. The model was evaluated in comparison to images reconstructed using another emerging technique called GRASP. Whereas more investigation is warranted, the results are promising, suggesting that CycleGAN could be a viable method for effective streak-reduction in clinical applications.

This research considers the problem of cooperatively identifying the active bands in a wideband spectrum using the sparse Fast Fourier Transform (sFFT). Existing research has focused primarily on Compressed Sensing (CS) and Multi-Coset (MC) sampling, but recent developments in the sFFT have shown that a sparsely occupied spectrum can be efficiently reconstructed using multiple co-prime analog-to-digital converters (ADC) that sample below the Nyquist rate. Specifically, this research utilizes the Robust Fast Fourier Aliasing-based Sparse Transform (R-FFAST) and extends this algorithm for use in cooperative wideband spectrum sensing (CWSS). Unlike previous approaches that implement the sFFT for spectrum sensing, the R-FFAST framework was developed and analyzed using the mutual coherence and the restricted isometry property (RIP) from CS theory. This leads to reliable support estimation in the presence of additive white Gaussian noise (AWGN) while mitigating the computational complexity of CS reconstruction algorithms. This research makes the following contributions. First, this research extends the signal model from single tones to multi-band signals with clustered support. Second, it shows that each stage in the R-FFAST front-end can be decomposed into individual nodes that form a fully distributed cooperative network. Lastly, this research empirically develops a constant false alarm rate (CFAR) detector that is used to identify the active frequency bins during the reconstruction process. The primary result of this research is showing that reliable spectrum detection is only possible when the average sampling rate of the cooperative network is greater than or equal to the sparsity of the spectrum. Simulation results are provided to demonstrate the effectiveness of the proposed framework and validate the findings of this research. / Electrical and Computer Engineering