The FFT is an efficient algorithm for computing the DFT. It drastically reduces the cost of implementing the DFT on digital computing systems. Nevertheless, the FFT is still computationally intensive, and continued technological advances of computers demand larger and faster implementations of this algorithm. Past attempts at producing high-performance, and small FFT implementations, have focused on custom hardware (ASICs and FPGAs). Ultimately, the most efficient have been single-chipped, streaming I/O, pipelined FFT architectures. These architectures increase computational concurrency through the use of hardware pipelining. Streaming I/O, pipelined FFT architectures are capable of accepting a single data sample every clock cycle. In principle, the maximum clock frequency of such a circuit is limited only by its critical delay path. The delay of the critical path may be decreased by the addition of pipeline registers. Nevertheless this solution gives diminishing returns. Thus, the streaming I/O, pipelined FFT is ultimately limited in the maximum performance it can provide. Attempts have been made to map the Parallel FFT algorithm to custom hardware. Yet, the Parallel FFT was formulated and optimized to execute on a machine with multiple, identical, processing elements. When executed on such a machine, the FFT requires a large expense on communications. Therefore, a direct mapping of the Parallel FFT to custom hardware results in a circuit with complex control and global data movement. This thesis proposes the Hybrid Architecture Parallel FFT (HAPFFT) as an alternative. The HAPFFT is an improved formulation for building Parallel FFT custom hardware modules. It provides improved performance, efficient resource utilization, and reduced design time. The HAPFFT is modular in nature. It includes a custom front-end parallel processing unit which produces intermediate results. The intermediate results are sent to multiple, independent FFT modules. These independent modules form the back-end of the HAPFFT, and are generic, meaning that any prexisting FFT architecture may be used. With P back-end modules a speedup of P will be achieved, in comparison to an FFT module composed solely of a single module. Furthermore, the HAPFFT defines the front-end processing unit as a function of P. It hides the high communication costs typically seen in Parallel FFTs. Reductions in control complexity, memory demands, and logical resources, are achieved. An extraordinary result of the HAPFFT formulation is a sublinear area-time growth. This phenomenon is often also called superlinear speedup. Sublinear area-time growth and superlinear speedup are equivalent terms. This thesis will subsequently use the term superlinear speedup to refer to the HAPFFT's outstanding speedup behavior. A further benefit resulting from the HAPFFT formulation is reduced design time. Because the HAPFFT defines only the front-end module, and because the back-end parallel modules may be composed of any preexisting FFT modules, total design time for a HAPFFT is greatly reduced

Metabolomics is the study of metabolomes, the sets of metabolites observed in living systems. Metabolism interconverts these metabolites to provide the molecules and energy necessary for life processes. Many disease processes, including cancer, have a significant metabolic component that manifests as differences in what metabolites are present and in what quantities they are produced and utilized. Thus, using metabolomics, differences between metabolomes in disease and non-disease states can be detected and these differences improve our understanding of disease processes at the molecular level. Despite the potential benefits of metabolomics, the comprehensive investigation of metabolomes remains difficult. A popular analytical technique for metabolomics is mass spectrometry. Advances in Fourier transform mass spectrometry (FT-MS) instrumentation have yielded simultaneous improvements in mass resolution, mass accuracy, and detection sensitivity. In the metabolomics field, these advantages permit more complicated, but more informative experimental designs such as the use of multiple isotope-labeled precursors in stable isotope-resolved metabolomics (SIRM) experiments. However, despite these potential applications, several outstanding problems hamper the use of FT-MS for metabolomics studies. First, artifacts and data quality problems in FT-MS spectra can confound downstream data analyses, confuse machine learning models, and complicate the robust detection and assignment of metabolite features. Second, the assignment of observed spectral features to metabolites remains difficult. Existing targeted approaches for assignment often employ databases of known metabolites; however, metabolite databases are incomplete, thus limiting or biasing assignment results. Additionally, FT-MS provides limited structural information for observed metabolites, which complicates the determination of metabolite class (e.g. lipid, sugar, etc. ) for observed metabolite spectral features, a necessary step for many metabolomics experiments. To address these problems, a set of tools were developed. The first tool identifies artifacts with high peak density observed in many FT-MS spectra and removes them safely. Using this tool, two previously unreported types of high peak density artifact were identified in FT-MS spectra: fuzzy sites and partial ringing. Fuzzy sites were particularly problematic as they confused and reduced the accuracy of machine learning models trained on datasets containing these artifacts. Second, a tool called SMIRFE was developed to assign isotope-resolved molecular formulas to observed spectral features in an untargeted manner without a database of expected metabolites. This new untargeted method was validated on a gold-standard dataset containing both unlabeled and 15N-labeled compounds and was able to identify 18 of 18 expected spectral features. Third, a collection of machine learning models was constructed to predict if a molecular formula corresponds to one or more lipid categories. These models accurately predict the correct one of eight lipid categories on our training dataset of known lipid and non-lipid molecular formulas with precisions and accuracies over 90% for most categories. These models were used to predict lipid categories for untargeted SMIRFE-derived assignments in a non-small cell lung cancer dataset. Subsequent differential abundance analysis revealed a sub-population of non-small cell lung cancer samples with a significantly increased abundance in sterol lipids. This finding implies a possible therapeutic role of statins in the treatment and/or prevention of non-small cell lung cancer. Collectively these tools represent a pipeline for FT-MS metabolomics datasets that is compatible with isotope labeling experiments. With these tools, more robust and untargeted metabolic analyses of disease will be possible.

Absorption bands responding to changes in fat, protein, and lactose concentrations in milk were determined. The effects of milk fat variation and lipolysis on the infrared spectrum were studied. Absorbances from 1283 to 1100 cm-1 correlated with fat, protein, and lactose concentration and showed a low response to milk fat variation and lipolysis. A Fourier transform infrared spectrometer equipped with an attenuated total internal reflectance cell was calibrated using these absorption band s, partial least squares statistics, and milk samples from herds in Minnesota. When the fat, protein, and lactose concentrations in these samples were predicted, the standard deviations of difference (reference - infrared) were .22, .06, and .02% . When the fat, protein, and lactose concentrations in a separate set of samples from herds in California were predicted, the standard deviations of difference were 1.23, .10, and .07%. Substitution of a 15 μm pathlength transmission cell for the attenuated total internal reflectance cell changed the standard deviations of difference to .07, .11, and .06% in the calibration (Minnesota) samples and .09, .10, and .16% in the validation (California) samples. Infrared spectroscopy was used to measure whey powder in an adulterated sample of nonfat dry milk. Mixtures of nonfat dry milk containing whey powder at various concentrations were analyzed using absorption bands between 1400 and 1200 cm-1 in the infrared spectrum. There was a strong correlation (r > .99) between predicted and measured concentrations of whey powder in adulterated samples. Accuracy was not affected by processing conditions , source of nonfat dry milk, and origin of whey powder. A rapid method for detecting soybean oil in process cheese was developed. The infrared spectrum of each sample was collected using an accessory designed for analysis of solid samples. A linear relationship fit (= .98) when the ratio of absorbance at 2957 and 2852 cm-1 was plotted versus percent adulteration.

The aim of this work was to use Fourier Transform Infrared Spectroscopy to characterize and identify bacteria of particular significance to the food industry. FT-IR spectroscopy is a rapid technique that can be applied to all groups of bacteria. The two objectives were to determine a suitable sampling procedure to record a spectrum and to determine a suitable statistical technique to identify characteristic regions of the spectrum associated with the genus and, potentially, the species. Pure cultures of bacteria were grown in broth, suspended in saline and dried to produce a film on a halide salt crystal. These films were then used to produce FT-IR spectra. In total, 80 spectra were recorded from seven genera, seven species and four strains of bacteria. Some of the spectra were considered to be too low in intensity to be included in statistical analysis. Data points from three specific windows of the remaining spectra were used to determine spectral distances between spectra. These spectral distances were used to perform cluster analysis using Ward's method, the Complete Linkage method and the Centroid method. The statistical analysis created successful clusters for several of the species used but was inconclusive overall in being able to distinguish between spectra at the genus, species and strain level. This may be due to inconsistent growth of bacteria and insufficient manipulation of the data. This study has shown the potential for FT-IR spectroscopy to be used to identify bacteria with significance for food but further development is needed to reproduce the consistent results demonstrated in current literature.

Early detection, diagnosis, and suitable treatment are known to significantly improve the chance of survival for breast cancer (BC) patients. To date, the most cost effective method for screening and early detection is screen-film mammography, which is also the only tool that has demonstrated its ability to reduce BC mortality. Full-field digital mammography (FFDM) is an extension of screen-film mammography that eliminates the need for film-processing because the images are detected electronically from their inception. Tomosynthesis is an emerging technology in digital mammography built on the FFDM framework, which offers an alternative to conventional two-dimensional mammography. Tomosynthesis produces three-dimensional (volumetric) images of the breast that may be superior to planar imaging due to improved visualization. In this work preliminary tomosynthesis data derived from cadaver breasts are analyzed, which includes volume data acquired from various reconstruction techniques as well as the planar projection data. The noise and power spectra characteristics analyses are the focus of this study. Understanding the noise characteristics is significant in the study of radiological images and in the evaluation of the imaging system, so that its degrading effect on the image can be minimized, if possible and lead to better diagnosis and optimal computer aided diagnosis schemes. Likewise, the power spectra behavior of the data are analyzed, so that statistical methods developed for digitized film images or FFDM images may be applied directly or modified accordingly for tomosynthesis applications. The work shows that, in general, the power spectra for three of the reconstruction techniques are very similar to the spectra of planar FFDM data as well as digitized film; projection data analysis follows the same trend. To a good approximation the Fourier power spectra obey an inverse power law, which indicates a degree of self-similarity. The noise analysis indicates that the noise and signal are dependent and the dependency is a function of the reconstruction technique. New approaches for the analysis of signal dependent noise were developed specifically for this work based on both the linear wavelet expansion and on nonlinear order statistics. These methods were tested on simulated data that closely follow the statistics of mammograms prior to the real-data applications. The noise analysis methods are general and have applications beyond mammography.

There is a crucial need for real time detection and diagnosis in digital mammography. To date, most computer aided analysis applications are software driven and normally require long processing times. Digital filtering is often the initial stage in processing mammograms for both automated detection and tissue characterization, which relies on Fourier analysis. In this research the main objective is to lay the groundwork for converting software driven mammography applications to hardware implementations by using Application-Specific Integrated Circuits (ASICs). The long-term goal is to increase processing speed. This research focuses on achieving the main objective by using one specific mammographic image processing application for demonstration purposes. ASICs offer high performance at the price of high development costs and are suitable for real time diagnosis. In this research, we develop a behavioral VHDL model of a specific filtering algorithm. Automatic Design Instantiation System (AUDI)8, a high level synthesis tool is used to automatically synthesize an RTL design from the model. A floating point behavioral component library is developed to support the synthesis of the filtering algorithm. The work shows that the hardware output is identical to the software driven output at when considering eight-bit accuracy and shows only rounding errors at higher storage capacities.

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