Symbolic dynamics is a current interest in the area of anomaly detection, especially in mechanical systems.  Symbolic dynamics reduces the overall dimensionality of system responses while maintaining a high level of robustness to noise.  Rolling element bearings are particularly common mechanical components where anomaly detection is of high importance.  Harsh operating conditions and manufacturing imperfections increase vibration innately reducing component life and increasing downtime and costly repairs.  This thesis presents a novel way to detect bearing vibrational anomalies through Symbolic Aggregate Approximation (SAX) in the two-dimensional time-frequency domain.  SAX reduces computational requirements by partitioning high-dimensional sensor data into discrete states.  This analysis specifically suits bearing vibration data in the time-frequency domain, as the distribution of data does not greatly change between normal and faulty conditions. Under ground truth synthetically-generated experiments, two-dimensional SAX in conjunction with Markov model feature extraction is successful in detecting anomalies (> 99%) using short time spans (< 0.1 seconds) of data in the time-frequency domain with low false alarms (< 8%).  Analysis of real-world datasets validates the performance over the commonly used one-dimensional symbolic analysis by detecting 100% of experimental anomalous vibration with 0 false alarms in all fault types using less than 1 second of data for the basis of 'normality'. Two-dimensional SAX also demonstrates the ability to detect anomalies in predicative monitoring environments earlier than previous methods, even in low Signal-to-Noise ratios. / Master of Science

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Active noise control (ANC) is a real-time process in which a system measures an external, unwanted sound source and produces a canceling waveform. The cancellation is due to destructive interference by a perfect copy of the received signal phase-shifted by 180 degrees. Existing active noise control systems process the incoming and outgoing audio on a sample-by-sample basis, requiring a high-speed digital signal processor (DSP) and analog-to-digital converters (ADCs) with strict timing requirements on the order of tens of microseconds. These timing requirements determine the maximum sample rate and bit size as well as the maximum attenuation that the system can achieve. In traditional noise cancellation systems, the general assumption is that all unwanted sound is indeterminate. However, there are many instances in which an unwanted sound source is predictable, such as in the case of a song. This thesis presents a method for active acoustic cancellation of a known audio signal using the frequency characteristics of the known audio signal compared to that of a sampled, filtered excerpt of the same known audio signal. In this procedure, we must first correctly locate the sample index for which a measured audio excerpt begins via the cross-correlation function. Next, we obtain the frequency characteristics of both the known source (WAVE file of the song) and the measured unwanted audio by taking the Fast Fourier Transform (FFT) of each signal, and calculate the effective environmental transfer function (degradation function) by taking the ratio of the two complex frequency-domain results. Finally, we attempt to recreate the environmental audio from the known data and produce an inverted, synchronized, and amplitude-matched signal to cancel the audio via destructive interference. Throughout the process, we employ many signal conditioning methods such as FIR filtering, median filtering, windowing, and deconvolution. We illustrate this frequency-domain method in Native Instruments’ LabVIEW running on the Windows operating system, and discuss its reliability, areas for improvement, and potential future applications in mobile technologies. We show that under ideal conditions (unwanted sound is a known white noise source, and microphone, loudspeaker, and environmental filter frequency responses are all perfectly flat), we can achieve a theoretical maximum attenuation of approximately 300 dB. If we replace the white noise source with an actual song and the environmental filter with a low-order linear filter, then we can achieve maximum attenuation in the range of 50-70 dB. However, in a real-world environment, with additional noise and imperfect microphones, speakers, synchronization, and amplitude-matching, we can expect to see attenuation values in the range of 10-20 dB.

When designing custom hardware to implement signal processing algorithms, it is important to select bitwidths that meet the minimum error requirements while minimizing implementation area. Larger bitwidths reduce error, but increase area, while selecting smaller bitwidths does the opposite. Finding the set of bitwidths that produces the smallest area that still meets the error requirements has been shown to be NP-hard. To address this problem, many heuristics have been developed. Unfortunately, they are not always well documented and do not have available source code. It is also di cult to know which algorithm to try to use. This thesis addresses these challenges in several ways. It provides the necessary background information to understand bitwidth optimization algorithms, as well as a survey of the existing literature. It also presents a new framework called Bitwidth Analysis Tool (BAT) built on the open source Ptolemy tool. This framework is designed to help implement and compare bitwidth optimization algorithms. Some existing algorithms are implemented within this new framework, and compared with each other on a variety of benchmarks. The comparison results verify that because the tested algorithms are heuristics, no single algorithm gives the best results in all cases. It is therefore important to test a variety of algorithms to try to find the best answer. The results also show existing algorithms and error models provide a good starting point, but existing error models do not yet provide sufficiently tight bounds to be useful in large complex systems.

Nuclear spectroscopy is an interdisciplinary subject of physics and electronics, which adopts state-of-the-art digital electronic technology and computer technology to analyze the information in ionizing radiation. The use of FPGAs shortens the development cycles of the digital circuit design and reduces system noise with compact electronics size. As a result, digital spectrometers with FPGAs are gaining popularity in research and industrial markets. The motivation behind this work was to replace conventional analog electronics with modern digital technology to provide an excellent energy resolution for different kinds of nuclear detectors and experiments. In this thesis, a SiPM-based scintillation detector is first designed based on the basic principles of ionizing radiation. The readout circuit of the detector is given in detail. Subsequently, a real-time DPP module is designed using the FPGA of Lattice. The system noise of the DPP is measured, compared, and analyzed after the hardware verification and implementation of digital algorithms to assess the capability of the DPP module. Afterward, digital pulse processing algorithms are investigated in detail to improve the performance of the designed digital module. The design and implementation of multipass moving average and trapezoidal filter are presented. The PZC and BLR are designed and implemented according to the analysis of the trapezoidal filter’s weakness to have a better energy resolution of the digital system. Algorithms are designed and implemented on a Simulink platform. Experimental results and analyses are provided at the end of this thesis. The acquired data are analyzed in real-time or by offline software. Spectra and resolutions are demonstrated of different detectors to evaluate the performance of digital module and algorithms implementation. The resolution of the scintillation detector can be obtained to 4.2%, which is almost the optimal value based on their datasheet. The implementations of digital algorithms are verified. Other applications are provided, such as coincidence and cosmic muons measurements.

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As a promising candidate to break the single-mode fiber capacity limit, mode-division multiplexing (MDM) explores the spatial dimension to increase transmission capacity in fiberoptic communication. Two linear impairments, namely loss and multimode interference, present fundamental challenges to implementing MDM. In this dissertation, techniques to resolve these two issues are presented. To de-multiplex signals subject to multimode interference in MDM, Multiple-InputMultiple-Output (MIMO) processing using adaptive frequency-domain equalization (FDE) is proposed and investigated. Both simulations and experiments validate that FDE can reduce the algorithmic complexity significantly in comparison with the conventional time-domain equalization (TDE) while achieving similar performance as TDE. To further improve the performance of FDE, two modifications on traditional FDE algorithm are demonstrated. i) normalized adaptive FDE is applied to increase the convergence speed by 5 times; ii) masterslave carrier recovery is proposed to reduce the algorithmic complexity of phase estimation by number of modes. Although FDE can reduce the computational complexity of the MIMO processing, due to large mode group delay (MGD) of FMF link and block processing, the algorithm still requires enormous memory and high hardware complexity. In order to reduce the required tap length (RTL) of the equalizer, differential mode group delay compensated fiber (DMGDC) has been proposed. In this dissertation, the analytical expression for RTL is derived for DMGDC systems under the weak mode coupling assumption. Instead of depending on the overall MGD of the link iii in DMGD uncompensated (DMGDUC) systems, the RTL of DMGDC systems depend on the MGD of a single DMGDC fiber section. The theoretical and numerical results suggest that by using small compensation step-size, the RTL of DMGDC link can be reduced by 2 orders of magnitude compared to DMGDUC link. To compensate the loss of different modes, multimode EDFAs are presented with reconfigurable multimode pumps. By tuning the mode content of the multimode pump, modedependent gain (MDG) can be controlled and equalized. A proto-type FM-EDFA which could support 2 LP modes was constructed. The experimental results show that by using high order mode pumps, the modal gain difference can be reduced. By applying both multimode EDFA and equalization techniques, 26.4Tb/s MDM-WDM transmission was successfully demonstrated. A brief summary and several possible future research directions conclude this dissertation.

Coherent detection with subsequent digital signal processing (DSP) is developed, analyzed theoretically and numerically and experimentally demonstrated in various fiber-optic transmission scenarios. The use of DSP in conjunction with coherent detection unleashes the benefits of coherent detection which rely on the preservation of full information of the incoming field. These benefits include high receiver sensitivity, the ability to achieve high spectral-efficiency and the use of advanced modulation formats. With the immense advancements in DSP speeds, many of the problems hindering the use of coherent detection in optical transmission systems have been eliminated. Most notably, DSP alleviates the need for hardware phase-locking and polarization tracking, which can now be achieved in the digital domain. The complexity previously associated with coherent detection is hence significantly diminished and coherent detection is once again considered a feasible detection alternative. In this thesis, several aspects of coherent detection (with or without subsequent DSP) are addressed. Coherent detection is presented as a means to extend the dispersion limit of a duobinary signal using an analog decision-directed phase-lock loop. Analytical bit-error ratio estimation for quadrature phase-shift keying signals is derived. To validate the promise for high spectral efficiency, the orthogonal-wavelength-division multiplexing scheme is suggested. In this scheme the WDM channels are spaced at the symbol rate, thus achieving the spectral efficiency limit. Theory, simulation and experimental results demonstrate the feasibility of this approach. Infinite impulse response filtering is shown to be an efficient alternative to finite impulse response filtering for chromatic dispersion compensation. Theory, design considerations, simulation and experimental results relating to this topic are presented. Interaction between fiber dispersion and nonlinearity remains the last major challenge deterministic effects pose for long-haul optical data transmission. Experimental results which demonstrate the possibility to digitally mitigate both dispersion and nonlinearity are presented. Impairment compensation is achieved using backward propagation by implementing the split-step method. Efficient realizations of the dispersion compensation operator used in this implementation are considered. Infinite-impulse response and wavelet-based filtering are both investigated as a means to reduce the required computational load associated with signal backward-propagation. Possible future research directions conclude this dissertation.

The open-source community is a valuable resource for many hobbyists and researchers interested in collaborating and contributing towards publicly available tools. In the area of field programmable gate arrays (FPGAs) this is no exception. Contributors seek to reverse-engineer the functions of large proprietary FPGA devices. An interesting challenge for open-source FPGA engineers has been reverse-engineering the operation and bitstreams of digital signal processing (DSP) blocks located in FPGAs. SymbiFlow is an open-source FPGA toolchain designed as a free alternative to proprietary computer-aided design tools like Xilinx’s Vivado. For SymbiFlow, mapping logical multipliers to DSP blocks and generating DSP block bitstreams has been left unimplemented for the Artix-7 family of FPGAs. This research seeks to rectify this shortcoming by introducing DSP information for the place and route functions into SymbiFlow. By delving into the SymbiFlow architecture definitions and creating functioning FPGA assembly code (FASM) files for Project X-Ray, a bitstream generator for Artix-7, we have been able to determine the desired output of the open-source Versatile Place & Route tool that will generate a working DSP bitstream. We diagnose and implement changes needed throughout the SymbiFlow toolchain, allowing for DSP design bitstreams to be successfully generated with open-source tools.