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This thesis examines applications of Digital Signal Processing to the analysis, transformation, and resynthesis of musical audio. First I give an overview of the human perception of music. I then examine in detail the requirements for a system that can analyse, transcribe, process, and resynthesise monaural polyphonic music. I then describe and compare the possible hardware and software platforms. After this I describe a prototype hybrid system that attempts to carry out these tasks using a method based on additive synthesis. Next I present results from its application to a variety of musical examples, and critically assess its performance and limitations. I then address these issues in the design of a second system based on Gabor wavelets. I conclude by summarising the research and outlining suggestions for future developments.

Time-compression overlap-add (TC-OLA) is presented as a novel method of communications over a (wireless) channel, which is shown to have benefits over other methods in some applications. TC-OLA is initially explored in an experimental context using a custom wideband software-defined radio (SDR) to gain insight into some of the possibilities of this method. Basic analysis is developed showing the processing gain, transmitted spectrum, and behaviour in fading channels. The method is considered as a candidate for low power wide area network (LPWAN) applications, highlighting the equivalent channel property, channel averaging, and ability to handle more simultaneous users in the uplink than other schemes in this application area.The method is then considered as an alternative to single carrier frequency domain equalization (SC-FDE) for ultrawideband (UWB) applications, where the ability to reduce or eliminate the cyclic prefix (CP) overhead while still using frequency domain equalization (FDE) techniques is highlighted. Additional application areas for this technology are briefly considered, including cognitive radio and radar. The process of patenting this technology is outlined in an appendix. The issued patent can be found through the United States Patent and Trademark Office (USPTO) as U.S. Patent 9,479,216. / Graduate

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Employing a combination of biochemistry and chemometrics, the field of metabolomics has the potential to reveal some very significant insights into biological pathways related to drugs and diseases. This thesis explores this field in its depths; specifically focusing on Nuclear Magnetic Resonance (NMR) based methods. The thesis begins with an exploration of the quantum level relationships of molecules, and how these coupling patterns evolve into an NMR spectrum. The thesis will describe the development of a simplified spin simulation algorithm to predict NMR spin coupling patterns that are computed in fractions of a second and to build mathematically relevant basis functions. Later in the thesis, the issue of baseline distortions of real NMR experimental data is addressed by the development of an automated baseline correction algorithm. Data reduction techniques are further analyzed to understand the importance of the quality of the data used in advanced chemometric methods. For analysis of the data, the use of simple univariate techniques applied to NMR spectra of urine is explored to determine statistically significant biomarkers between disease states in asthma. More advanced statistics in the way of multivariate models, namely Partial Least Squares – Discriminant Analysis (PLS-DA), were used to build predictive models of Streptococcus pneumoniae pneumonia from NMR spectra of urine. Potential characteristics of the data that may invalidate assumptions required in our models were accounted for, such as ensuring the statistical normality of the S. pneumoniae pneumonia data by using log transformations. After the analysis, focus was given to the use of unique visualization techniques to further explore the complex relationships that exist between samples and variables, and relationships between variables. As will be made evident, this thesis deals with the basic physics of an NMR signal to building highly sophisticated models to help understand the NMR spectra from complex mixtures. All of these notions are important in the objective to garner the most information provided through an NMR experiment, as such to aid in the discovery of biochemical knowledge. / Process Control

The use of two dimensional (2D) digital filters for real-time 2D data processing has found important practical applications in many areas, such as aerial surveillance, satellite imaging and pattern recognition. In the case of military operations, real-time image pro-cessing is extensively used in target acquisition and tracking, automatic target recognition and identi cation, and guidance of autonomous robots. Furthermore, equal opportunities exist in civil industries such as vacuum cleaner path recognition and mapping and car collision detection and avoidance. Many of these applications require dedicated hardware for signal processing. It is not efficient to implement 2D digital filters using a single processor for real-time applications due to the large amount of data. A multiprocessor implementation can be used in order to reduce processing time. Previous work explored several realizations of 2D denominator separable digital filters with minimal throughput delay by utilizing parallel processors. It was shown that regardless of the order of the filter, a throughput delay of one adder and one multiplier can be achieved. The proposed realizations have high regularity due to the nature of the processors. In this thesis, all four realizations are implemented in a Field Programming Gate Array (FPGA) with floating point adders, multipliers and shift registers. The implementation details and design trade-offs are discussed. Simulation results in terms of performance, area and power are compared. From the experimental results, realization four is the ideal candidate for implementation on an Application Specific Integrated Circuit (ASIC) since it has the best performance, dissipates the lowest power, and uses the least amount of logic when compared to other realizations of the same filter size. For a filter size of 5 by 5, realization four can produce a throughput of 16.3 million pixels per second, which is comparable to realization one and about 34% increase in performance compared to realization one and two. For the given filter size, realization four dissipates the same amount of dynamic power as realization one, and roughly 54% less than realization three and 140% less than realization two. Furthermore, area reduction can be applied by converting floating point algorithms to fixed point algorithms. Alternatively, the denormalization and normalization stage of the floating point pipeline can be eliminated and fused together in order to save hardware resources.

Power measurement is important for various purposes such as revenue metering, power quality improvement, and direct load control. Various algorithms for power measurement have been proposed in the time domain, which implies a simple instrumentation, but more useful power formulations have been derived in the frequency-domain approach which would require appropriate sampling and measurement techniques to avoid long delay in processing voltage and current signals. The aim of this thesis to implement a measurement instrument that can measure the power components digitally and efficiently under sinusoidal and non-sinusoidal situations. We will use a high performance digital signal processing (DSP) chip and adopt a frequency domain based algorithm for the computation of power elements. The measurement system is expected to offer both high speed and accuracy, and can show wide spectra limited only by the sampling frequency.

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