The main advantage of wavelet transform relative to its Fourier analysis counterpart is its suitability to deal with transient signals. Furthermore, wavelet packet transform has very good frequency analytic ability with the result that it is developing in very fast speed and widespread researched and used in industry and academia. We study the characteristics of fiber optic sensors by applying wavelet transform. Hence, in this paper, the traditional Fourier analysis is taken as a basis, and the wavelet packet analysis is taken as a comparison. The major objects include: (1) calibration of hydrophones; (2) vibration measurement. In calibration of hydrophones, the experimental results show a 2.72 dB re V/£gPa inaccuracies and a 5.3 dB re V/£gPa standard deviation by Fourier analysis, but 0.5 dB inaccuracies and 1.6 dB re V/£gPa standard deviation by wavelet packet analysis. It shows that the wavelet packet analysis has better analytic ability than that of traditional Fourier analysis. In vibration measurement, we utilize FBG interferometers to measure stable vibration. The experimental results denote that wavelet packet analysis has excellent frequency analytic ability as Fourier analysis. Besides, in obtaining transient characteristic signals induced by falling stones, the results appear that wavelet packet analysis has better resolution and identification capability relative to Fourier analysis.

Digital options, the basic building blocks for valuing complex financial assets, they play an important role in options valuation and hedging. We survey the digital options pricing formula under diffusion processes and jump-diffusion processes. Since the existent first-touch digital options pricing formulas with jump-diffusion processes are all in their Laplace transform of the option value. To inverse the Laplace transforms is critical when doing options valuation. Therefore, we adopt a phase-type jump-diffusion model which is developed by Chen, Lee and Sheu [2007] as our main model, and use FFT inversion to get the first-touch digital option price under (2,2)-factor exponential jump-diffusion processes.

Thesis (M.S.)--Worcester Polytechnic Institute. / Keywords: cartilage, tendon, light scattering. Includes bibliographical references (p. 60-61).

Thesis (M.S.)--West Virginia University, 2002. / Title from document title page. Document formatted into pages; contains xiii, 187 p. : ill. (some col.). Includes abstract. Includes bibliographical references (p. 171-175).

Thesis (Ph.D)--Chemical Engineering, Georgia Institute of Technology, 2009. / Committee Chair: Sujit Banerjee; Committee Co-Chair: Wm. James Frederick, Jr.; Committee Member: John D. Muzzy; Committee Member: Kristiina Iisa; Committee Member: Preet Singh. Part of the SMARTech Electronic Thesis and Dissertation Collection.

Variable-temperature Fourier transform infrared (VT-FTIR) spectroscopy in conjunction with 2D correlation analysis was employed to study the unfolding of aspartate transcarbamylase (ATCase) and its individual subunits. The regulatory subunit (RSU) was uniformly labeled with 13C/15N and then reconstituted with the unlabeled catalytic subunit (CSU) to form the holoenzyme. The activity of the holoenzyme was shown to be unaffected by the isotopic labeling of the RSU. The VT-FTIR investigation of the isolated CSU and the CSU in the holoenzyme revealed that the CSU is more thermally stable when bound to the RSU (i.e., in the holoenzyme). The RSU also showed more thermal stability when bound to the CSU. The sequences of events leading to the unfolding of the isolated CSU and RSU and the CSU in the holoenzyme were deduced by 2D correlation analysis of the VT-FTIR spectra. The results for the isolated CSU demonstrated that beta-sheets unfold first, followed by a-helices and then turns, and finally aggregates form. The sequence of unfolding of the RSU showed an increase of turns followed by a loss of intramolecular beta sheets, then a loss of alpha-helices and the formation of aggregates. The CSU in the holoenzyme exhibited a slightly different unfolding pathway and was observed to unfold subsequent to the unfolding of the RSU, consistent with the two thermal transitions observed by differential scanning calorimetry.

Infrared spectra of microbial cells are highly specific, fingerprint-like signatures which can be used to differentiate microbial species and strains from each other. In this study, the potential applicability of Fourier transform infrared (FTIR) spectroscopy for the classification of yeast strains in terms of their biological taxonomy, their use in the production of wine, beer, and bread, and their sensitivity to killer yeast strains was investigated. Sample preparation, spectral data preprocessing methods and spectral classification techniques were also investigated. All yeast strains were grown on a single growth medium. The FTIR spectra were baseline corrected and the second derivative spectra were computed and employed in spectral analysis. The classification accuracy was improved when the principal component spectra (calculated from the second derivative spectra) were employed rather than the second derivative spectra or raw spectra alone. Artificial neural network (ANN) with 10 units in the input layer and 12 units in the hidden layer produced a robust prediction model for the identification of yeasts. Cluster analysis was employed for the classification of yeast strains in terms of their use in the production of wine, beer, and bread and in terms of their sensitivity to killer yeast strains. The optimum region for the classification in the former case was found to be between 1300 and 800 cm-1 in the infrared spectrum whereas the optimum region for the classification of yeast strains in terms of their sensitivity was between 900 and 800 cm-1 . The results of this work demonstrated that FTIR spectroscopy could be successfully employed for the classification and identification of yeast strains with minimal sample preparation.

Fourier transform near-infrared (FT-NIR) spectroscopy was investigated as a means of quantitative analysis of edible fats and oils. Initially, a method of simultaneously determining the cis and trans content, iodine value and saponification number of neat fats and oils using a heated transmission flow cell was developed. Two partial least squares (PLS) calibrations were devised, a process-specific calibration based on hydrogenated soybean oil and a more generalized calibration based on many oil types, the latter able to analyze oils from a variety of sources accurately and reproducibly. Methodology for the quantitative determination of the peroxide value (PV) of edible oils using a novel glass-vial sample handling system was subsequently developed, based on the stoichiometric reaction of triphenylphosphine with hydroperoxides to form triphenylphosphine oxide. The PV calibration was derived using PLS regression, and the results of a validation study demonstrated that PV could be quantitated accurately if a normalization routine was used to compensate for the inherent dimensional variability of the vials. The vial sample handling system was then used in the development of PLS IV calibrations for the process analysis of commercial oil samples, and these samples were also used to evaluate a global IV calibration devised by Bomem Inc. The discriminant features available through PLS were shown to enhance the accuracy of the IV predictions by facilitating the selection of the most appropriate calibrations based on the spectral characteristics of closely related oils. The predictions obtained using the global IV calibration provided clear evidence that a generalized calibration based on a large and varied selection of oils could provide a means of IV determination by FT-NIR spectroscopy. Subsequently, a generalized FT-NIR trans calibration was developed and shown to yield trans values that were in good agreement with those obtained by the AOCS mid-FTIR single-bounce hori

An industrial Fourier transform infrared (FTIR) milk analyser has been adapted for the proximate analysis of fresh or cooked meat and meat products. Stable freeze-dried samples of ground beef and bologna were prepared for the calibration of an FTIR spectrometer equipped with a 37-mum transmission cell maintained at a constant temperature of 65°C and were analysed for fat, protein, moisture, and ash by the official methods of analysis of the Association of Official Analytical Chemists (AOAC) prior to instrumental measurement. The requirement to prepare a "milk-like" emulsion of meat for FTIR analysis led to the development of two prototype high-pressure homogenizers specifically designed to produce analytical volumes of emulsions in which the largest residual colloids present in suspension would have dimensions smaller than 1 mum. Emulsified samples were examined by transmission electron microscopy and laser light scattering spectroscopy to determine the size distribution of fat globules and the dimensions of the residual insoluble fragments of protein. / "Milk-like" emulsions of meat passed three times through a high-pressure homogenizer operating at 20,000 psi (138 MPa) had an average fat globule diameter of less than 320 nm. Also, the use of high-pressure homogenization eliminated the need to filter out insoluble proteins from connective tissues prior to the infrared analysis, resulting in a more accurate determination of the protein content in the meat samples. The results of validation studies conducted with both fresh and freeze-dried samples demonstrated that it is possible to analyse meat samples simultaneously for fat, protein, carbohydrates and moisture with good accuracy in approximately 7½; minutes per sample employing existing FTIR instrumentation used for the routine analysis of milk and dairy products.

A novel and rapid method was developed to monitor the autoxidation of edible oils by Fourier transform infrared (FTIR) spectroscopy with the use of disposable polymer infrared (PIR) cards having a microporous polytetrafluoroethylene (PTFE) sample substrate. Under conditions of mild heating (~58°C) and aeration, both model triacylglycerols (TAGS) and edible oils applied onto the PIR cards underwent rapidly accelerated oxidation. In order to compare the oxidative stability of samples on the PIR cards in terms of the time required to reach a peroxide value (PV) of 100 mequiv/kg oil, matching the end-point measured in the standard active oxygen method (AOM), an absorbance slope factor (ASF) was determined to relate changes in hydroperoxide (ROOH) absorbance (peak maximum found within the range of 3500--3200 cm-1 ) to PV. Similar ASF values were found for the four edible oils tested (safflower, canola, sunflower, and extra virgin olive oil), permitting determination of a pooled, universally applicable ASF value of 0.0526 mAbs/PV.