This thesis develops a generic framework based on the Fourier transform for pricing and hedging of various options in equity, commodity, currency, and insurance markets. The pricing problem can be reduced to solving a partial integro-differential equation (PIDE). The Fourier Space Time-stepping (FST) framework developed in this thesis circumvents the problems associated with the existing finite difference methods by utilizing the Fourier transform to solve the PIDE. The FST framework-based methods are generic, highly efficient and rapidly convergent. The Fourier transform can be applied to the pricing PIDE to obtain a linear system of ordinary differential equations that can be solved explicitly. Solving the PIDE in Fourier space allows for the integral term to be handled efficiently and avoids the asymmetrical treatment of diffusion and integral terms, common in the finite difference schemes found in the literature. For path-independent options, prices can be obtained for a range of stock prices in one iteration of the algorithm. For exotic, path-dependent options, a time-stepping methodology is developed to handle barriers, free boundaries, and exercise policies. The thesis includes applications of the FST framework-based methods to a wide range of option pricing problems. Pricing of single- and multi-asset, European and path-dependent options under independent-increment exponential Levy stock price models, common in equity and insurance markets, can be done efficiently via the cornerstone FST method. Mean-reverting Levy spot price models, common in commodity markets, are handled by introducing a frequency transformation, which can be readily computed via scaling of the option value function. Generating stochastic volatility, to match the long-term equity options market data, and stochastic skew, observed in currency markets, is addressed by introducing a non-stationary extension of multi-dimensional Levy processes using regime-switching. Finally, codependent jumps in multi-asset models are introduced through copulas. The FST methods are computationally efficient, running in O(MN^d log_2 N) time with M time steps and N space points in each dimension on a d-dimensional grid. The methods achieve second-order convergence in space; for American options, a penalty method is used to attain second-order convergence in time. Furthermore, graphics processing units are utilized to further reduce the computational time of FST methods.

This thesis presents a method for dynamic characterization of MEMS structures and discuses parameters that affect its measurements and techniques to improve them. Current methods of non-contact, laser based vibration measurement require special and expensive instruments. The method used in this thesis on the other hand, relies on Fast Fourier Transform analysis of blurred images captured using conventional cameras. The Fourier series analysis and transformation are introduced. Basic concepts of blur image analysis and associated technical terms are described. Step by step data extraction process for Fourier analysis of blurred images and results such as amplitude, attenuation, signal to noise ratio and Bessel curve are explained. Macro and micro scale experiments are designed and used to determine the effect and significance of different parameters on signal-to-noise ratio of extracted results. For this purpose geometrical parameters of macro scale combs such as length, width and duty cycle are varied across a considerable range and tests results are examined. In addition to the experiments, MATLAB code is used to model environmental effects such as addition of noise or changes of brightness. In micro scale experiments, extra patterns are created using Focused Ion Beam and etching process. Test and comparison of modified micro structures with unpatterned structures show improvement in signal to noise ratio especially in environments with high level of noise.

As part of the ExoMars space programme, the 2016 Trace Gas Orbiter mission was announced. The Martian Atmospheric Trace Molecule Occultation Spectrometer (MATMOS) was a proposed Fourier transform spectrometer and solar imager concept pair that would provide for trace gas detection and aerosol observation of the Martian atmosphere. Martian aerosols – namely CO2 crystals, water-ice crystals, and dust – have been observed during past missions; however, observations have failed to fully characterize their physical and optical properties. This thesis presents an analysis of the ability of the proposed imager to determine the pointing of the spacecraft independent of the spectrometer. Furthermore, proof of concept is presenting showing the ability to, in laboratory conditions, characterize the precision and stability of the imager. Finally, window regions in the transmittance spectrum of the Martian atmosphere are determined simulating the Martian atmosphere and viewing geometry.

The Orion Molecular Cloud (OMC) is the nearest, and thus most studied, star forming region to the Earth. To date, most of the studies conducted at submillimetre wavelenths have focused on the spectral line analysis using high resolution heterodyne recievers. However, the role of dust, which is known to be important in the evolution of the interstellar medium, can only be studied through its continuum emission. This thesis presents the first results obtained using a Fourier Transform Spectrometer (FTS) at the James Clerk Maxwell Telescope to study, simultaneously, the continuum and line components of emission on the OMC. / xiii, 139 leaves : ill. (some col.) ; 29 cm.

The European Space Agency's Herschel Space Observatory is comprised of three cryogenically cooled instruments commissioned to explore the far infrared/submillimetre universe. The Spectral and Photometric Imaging REceiver (SPIRE) is one of Herschel's instruments and consists of a three band imaging photometer and a two band imaging spectrometer. Canada is involved in the SPIRE project through provision of instrument development hardware and software, mission flight software, and support personnel. This thesis discusses Fourier transform spectroscopy (FTS) and FTS data processing. A detailed discussion is included on FTS phase correction, with results presented from the optimization of an enhanced Forman phase correction routine developed for this work. This thesis discusses the design, verification, and use of the hardware and software provided by Dr. Naylor's group as it relates to SPIRE verification testing. Results of the photometer characterization are presented. The current status of SPIRE and its future schedule is also discussed. / xvii, 239 leaves : ill. (some col.) ; 28 cm.

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The utility of focal-plane-array Fourier transform infrared (FPA-FTIR) spectroscopy as a rapid method for the differentiation of antibiotic resistant foodborne pathogens was studied. / Optimum spectral acquisition and processing parameters as well as appropriate film thickness of bacterial films were empirically established for the discrimination between two Shigella species (S. flexneri and S sonnei) in order to optimize the scanning parameters of an FPA-FTIR spectrometer. A detailed study of the potential of FPA-FTIR spectroscopy for the discrimination between antibiotic resistant and sensitive strains from two Salmonella species (S. Typhimurium and S. Heidelberg) was subsequently undertaken. The results of these studies demonstrated that the infrared spectra recorded by an FPA-FTIR spectrometer contained sufficient information to differentiate between antibiotic resistant and sensitive strains of Salmonella. Accordingly, FPA-FTIR spectroscopy may potentially serve as a high-throughput technique for the identification of foodborne as well as antibiotic resistant bacteria. / Interpretation of the regions selected in relation to the different resistance mechanisms would require more detailed studies. However, the identification of specific biochemical markers based on such spectral interpretation is generally not feasible owing to the complexity of the FTIR spectra of microorganisms.

New Fourier transform infrared (FTIR) approaches for the quantitative determination of peroxide value (PV) and isolated trans analyses were investigated and developed. The FTIR-PV methods investigated were all based on the stoichiometric reaction of hydroperoxides and triphenylphosphine (TPP) which converts TPP to triphenylphosphine oxide (TPPO). A reference transmission cell (100 mum) method was developed based on the use of a unique TPPO absorption at 542 cm-1. This method covered PV values from 0--15 PV and was shown to be superior in accuracy and reproducibility to the standard American Oil Chemists Society (AOCS) iodometric method. Subsequently, the utility of disposable polyethylene cards, normally used only for qualitative analyses, was investigated for quantitative PV determination. A quantitative IR card method was successfully developed and shown to serve as a very simple, rapid and alternative means of carrying out PV analyses. TPP-impregnated cards were able to reproduce the transmission cell PV results to +/-1.12 PV, while the unimpregnated card was slightly more accurate (+/-0.92 PV). A third FTIR-PV method was developed specifically for the at-line monitoring of high PV fatliquors and employed a germanium attenuated total reflectance sample handling accessory. This method hinged on the use of a TPPO absorption band at 1118 cm-1, normally off scale when pathlengths of >3 mum are used, but is suited to the analysis of oils having very high PVs (>250). The successful quantitative use of the disposable polyethylene IR card to PV led to its study for the quantitative FTIR determination of the isolated trans content of fats and oils and margarines. The polyethylene card was shown to unique and useful properties, tending to inhibit fat crystallization and its inability to retain moisture. These two properties allowed trans determination to be carried out on melted, high trans fats, without heating the polyethylene substrate and also to analyze margarines

The infrared spectra of 14 bacteria were recorded by Fourier Transform Infrared (FTIR) spectroscopy. The effects of changes in growth conditions, such as temperature, growth medium, and incubation time, sampling conditions on the reproducibility of the spectra were investigated. The spectra of bacteria suspended in saline solution, in D$ sb2$O-saline and on plate films were obtained and stored in separate spectral libraries. The application of library search routines for differentiation and identification of the 14 bacteria was investigated. The spectral regions used for the library search include 1750-1560 cm$ sp{-1}$ and 1480-960 cm$ sp{-1}$, which contain bands mainly associated with proteins (secondary structure), lipids, and polysaccharides. An index produced by the library search, which indicates how much an "unknown spectrum" matches a library spectrum, is suggested as a criterion for the differentiation and identification of bacteria. A correct identification of five unknown samples shows the feasibility of using spectral library searching routines for identification of bacteria down to the species level by FTIR spectroscopy. This technique is rapid, easier, and more efficient than conventional microbiological and biochemical methods. Quantitative analysis of a mixture of Escherichia coli and Staphylococcus aureus by the partial-lest-square (PLS) technique was also evaluated. The analytical error was about 10%.

The utility of single-bounce attenuated total reflectance (SB-ATR) and heterospectral two-dimensional correlation spectroscopy (H2D-CS) in quantitative analysis by Fourier transform infrared (FTIR) spectroscopy was investigated by exploring several potential applications of these techniques. Enzymatic hydrolysis of lactose in milk was monitored by SB-ATR/FTIR spectroscopy, and changes in the concentrations of glucose, galactose and lactose during the process were successfully measured quantitatively. SB-ATR/FTIR spectroscopy was shown also to perform comparably to Fourier transform near-infrared (FT-NIR) spectroscopy for the determination of the alcohol content of distilled liquors and better than FT-NIR spectroscopy and comparably to transmission FTIR spectroscopy for the analysis of alcohol, total reducing sugar, total acidity and pH in wines. In addition, a set of 149 pre-analyzed wine samples was employed to develop and validate an SB-ATR/FTIR calibration for 11 different parameters and constituents in wines with the use of partial-least-squares (PLS) regression, demonstrating the potential utility of this method in the routine analysis of wines. The application of SB-ATR/FTIR spectroscopy and H2D-CS in the selection of wavelengths for multiple linear regression (MLR) calibration for FT-NIR analysis of ternary aqueous solutions of fructose, glucose and galactose was also investigated. NIR wavelengths were identified for the three sugars by H2D-CS of the SB-ATR/FTIR spectra of binary sugar solutions in relation to their FT-NIR spectra. An MLR calibration developed based on these wavelengths gave better results than PLS calibrations and comparable results to those obtained by MLR using wavelengths selected by examination of 1st and 2nd derivative spectra. H2D-CS was extended to include 2D correlations between high-pressure liquid chromatography (HPLC) and SB-ATR/FTIR data for the purpose of identifying HPLC peaks without the need to isolate the eluted compounds. The potential utility of this approach, termed spectroscopic/chromatographic 2D correlation (SC2D-C), was investigated by generating FTIR slice spectra corresponding to the HPLC peaks of wines spiked with sucrose, glucose and fructose and comparing them to 404 reference spectra in an IR spectral library. It was found that these constituents were correctly identified provided there was sufficient random variability of their concentrations in the samples analyzed.