A fixed terrestrial wireless system such as the Microwave Multi-channel Distribution Service (MMDS) can be used as the ``last mile' to provide a high speed Internet connection from a base station to a home in a rural or suburban residential area. Such a broadband wireless system works very well under line-of-sight transmission. It works quite well even if the line-of-sight is obstructed with a large number of trees. However, when trees obstruct the line-of-sight, under conditions of wind, the user may experience loss of the RF signal from time to time. This is especially true under gusty conditions. As part of this research a high precision DSP-based measuring system is devised to accurately measure and characterize the distortions caused by tree foliage on the RF line-of-sight signal. The approach is to digitally generate a signal composed of several tones, up-convert the signal to 2.5 GHz and send it through tree foliage to a receiver where the signal is down-converted and sampled for a duration of five seconds. The samples collected are processed using Matlab to compute the temporal amplitude and phase variations of the tones. The measurement system provides estimates of the amplitude and phase of the receive tones with a time resolution of 3.2 ms. The standard deviation of the amplitude estimates is 0.3\% of the actual amplitude of the tones and the standard deviation of the phase estimates is 0.23 degree. This accuracy is obtained when the signal-to-noise ratio of the receive signal is greater than 20 dB. Measurement in the field with tree foliage in the line-of-sight shows that the swaying of the branches in the wind can cause rapid signal fading. This research determines the type of fade, the depth and duration of the fade, as well as the fading rate.

A high-resolution infrared Fourier Transform Spectrometer (FTS) has been operational at the Toronto Atmospheric Observatory (TAO)since May 2002. An optimal estimation retrieval technique is used to analyse the observed spectra and provide regular total and partial column measurements of trace gases in the troposphere and stratosphere as part of the Network for the Detection of Atmospheric Composition Change. The quality of these results were assessed through two ground-based validation campaigns, comparisons with three satellite instruments, and comparison with a three-dimensional chemical transport model. The two ground-based campaigns involved two lower-resolution FTS instruments: the University of Toronto FTS and the Portable Atmospheric Research Interferometric Spectrometer for the Infrared. The first campaign took place over the course of four months and is the longest side-by-side intercomparison of ground-based FTS instruments, to date. The second campaign was more focused and involved all three instruments measuring over a two-week period. Simultaneous measurements of O3, HCl, N2O, and CH4 were recorded and average total column differences were all < 3.7% in the extended campaign, and < 4.5% in the focused campaign. Satellite-based comparisons were done with the SCanning and Imaging Absorption spectroMeter for Atmospheric CHartographY (SCIAMACHY), the Atmospheric Chemistry Experiment Fourier Transform Spectrometer (ACE-FTS), and the Optical Spectrograph and InfraRed Imager System (OSIRIS). Total column CO, CH4, and N2O compared with SCIAMACHY all had average differences < 10% with results from the TAO-FTS being as good as, or better, than that of other instruments. Validation with the ACE-FTS showed that average partial columns of O3, NO2, N2O, CH4, and HCl were within 10% while observations of CO and NO each had an average bias of about 25%. Comparisons of monthly average partial column O3 and NO2 with OSIRIS were highly correlated (R = 0.82-0.97) with monthly mean differences of < 3.1% for O3 and < 2.6% for NO2. Finally, comparisons with the GEOS-Chem chemical transport model revealed that the model consistently over-estimates tropospheric columns of CO and C2H6 observed at TAO. It was determined that the enhanced CO values were partially due to the North American emissions specified in the model, but more work must be done in the future if the source of this discrepancy is to be fully explained.

The Fast Fourier Transform (FFT) has been used in many scientific and engineering applications. The use of FFT for financial derivatives has been gaining momentum in the recent past. In this thesis, i) we have improved a recently proposed model of FFT for pricing financial derivatives to help design an efficient parallel algorithm. The improved mathematical model put forth in our research bridges a gap between quantitative approaches for the option pricing problem and practical implementation of such approaches on modern computer architectures. The thesis goes further by proving that the improved model of fast Fourier transform for option pricing produces accurate option values. ii) We have developed a parallel algorithm for the FFT using the classical Cooley-Tukey algorithm and improved this algorithm by introducing a data swapping technique that brings data closer to the respective processors and hence reduces the communication overhead to a large extent leading to better performance of the parallel algorithm. We have tested the new algorithm on a 20 node SunFire 6800 high performance computing system and compared the new algorithm with the traditional Cooley-Tukey algorithm. Option values are calculated for various strike prices with a proper selection of strike-price spacing to ensure fine-grid integration for FFT computation as well as to maximize the number of strikes lying in the desired region of the stock price. Compared to the traditional Cooley-Tukey algorithm, the current algorithm with data swapping performs better by more than 15% for large data sizes. In the rapidly changing market place, these improvements could mean a lot for an investor or financial institution because obtaining faster results offers a competitive advantages. / October 2004

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Remote sensing of atmospheric gases improves our understanding of the state and evolution of the Earth’s environment. At the beginning of the thesis, the basic principles for the retrieval of concentrations of atmospheric gases from spectra are presented with a focus on ground-based observations. An overview of the characteristic features of different platforms, viewing geometries, measurement sites, and Fourier Transform Spectrometers (FTSs) used in the measurements are provided. The thesis covers four main projects. The first study of the global distribution of atmospheric phosgene was carried out using a total of 5614 measured profiles from the satellite-borne Atmospheric Chemistry Experiment FTS (ACE-FTS) spanning the period February 2004 through May 2006. The phosgene concentrations display a zonally symmetric pattern with the maximum concentration located approximately over the equator, at about 25 km in altitude, and the concentrations decrease towards the poles. A layer of enhanced concentration of phosgene spans the lower stratosphere at all latitudes, with volume mixing ratios of 20-60 pptv. The reasons for the formation of the phosgene distribution pattern are explained by the insolation, lifetime of phosgene and the Brewer-Dobson circulation. The ACE observations show lower phosgene concentrations in the stratosphere than were obtained from previous observations in the 1980s and 1990s due to a significant decrease in source species. The Portable Atmospheric Research Interferometric Spectrometer for the Infrared (PARIS-IR) is a copy of the ACE-FTS that was designed for ground-based and balloon-borne measurements. The first balloon flight was part of the Middle Atmosphere Nitrogen TRend Assessment (MANTRA) 2004 balloon payload. Some useful engineering information was obtained on the thermal performance of the instrument during the flight. As part of the MANTRA program, a ground-based inter-instrument comparison campaign was conducted with the objective of assessing instrument performance, and evaluating data processing routines and retrieval codes. PARIS-IR provides similar quality results for stratospheric species as does the University of Toronto FTS. An advanced study was carried out for the Carbon Cycle science by Fourier Transform Spectroscopy (CC-FTS) mission, which is a proposed future satellite mission to obtain a better understanding of the sources and sinks of greenhouse gases in the Earth’s atmosphere by monitoring total and partial columns of CO2, CH4, N2O, and CO in the near infrared together with the molecular O2 column. To evaluate the spectral regions, resolution, optical components, and spectroscopic parameters required for the mission, ground-based Fourier transform spectra, recorded at Kiruna, Kitt Peak, and Waterloo, were used. Dry air volume mixing ratios of CO2 and CH4 were retrieved from the ground-based observations. A FTS with a spectral resolution of 0.1 cm-1, operating between 2000 and 15000 cm-1, is suggested as the primary instrument for the mission. Further progress in improving the atmospheric retrievals for CO2, CH4 and O2 requires new laboratory measurements to improve the spectroscopic line parameters. Atmospheric observations were made with three FTSs at the Polar Environment Atmospheric Research Laboratory (PEARL) during spring 2006. The vertical column densities of O3, HCl, HNO3, HF, NO2, ClONO2 and NO from PARIS-IR, the Eureka DA8 FTS, and the ACE-FTS show good agreement. Chorine activation and denitrification in the Arctic atmosphere were observed in the extremely cold stratosphere near Eureka, Nunavut, Canada. The observed ozone depletion during the 2006 campaign was attributed to chemical removal.

Remote sensing of atmospheric gases improves our understanding of the state and evolution of the Earth’s environment. At the beginning of the thesis, the basic principles for the retrieval of concentrations of atmospheric gases from spectra are presented with a focus on ground-based observations. An overview of the characteristic features of different platforms, viewing geometries, measurement sites, and Fourier Transform Spectrometers (FTSs) used in the measurements are provided. The thesis covers four main projects. The first study of the global distribution of atmospheric phosgene was carried out using a total of 5614 measured profiles from the satellite-borne Atmospheric Chemistry Experiment FTS (ACE-FTS) spanning the period February 2004 through May 2006. The phosgene concentrations display a zonally symmetric pattern with the maximum concentration located approximately over the equator, at about 25 km in altitude, and the concentrations decrease towards the poles. A layer of enhanced concentration of phosgene spans the lower stratosphere at all latitudes, with volume mixing ratios of 20-60 pptv. The reasons for the formation of the phosgene distribution pattern are explained by the insolation, lifetime of phosgene and the Brewer-Dobson circulation. The ACE observations show lower phosgene concentrations in the stratosphere than were obtained from previous observations in the 1980s and 1990s due to a significant decrease in source species. The Portable Atmospheric Research Interferometric Spectrometer for the Infrared (PARIS-IR) is a copy of the ACE-FTS that was designed for ground-based and balloon-borne measurements. The first balloon flight was part of the Middle Atmosphere Nitrogen TRend Assessment (MANTRA) 2004 balloon payload. Some useful engineering information was obtained on the thermal performance of the instrument during the flight. As part of the MANTRA program, a ground-based inter-instrument comparison campaign was conducted with the objective of assessing instrument performance, and evaluating data processing routines and retrieval codes. PARIS-IR provides similar quality results for stratospheric species as does the University of Toronto FTS. An advanced study was carried out for the Carbon Cycle science by Fourier Transform Spectroscopy (CC-FTS) mission, which is a proposed future satellite mission to obtain a better understanding of the sources and sinks of greenhouse gases in the Earth’s atmosphere by monitoring total and partial columns of CO2, CH4, N2O, and CO in the near infrared together with the molecular O2 column. To evaluate the spectral regions, resolution, optical components, and spectroscopic parameters required for the mission, ground-based Fourier transform spectra, recorded at Kiruna, Kitt Peak, and Waterloo, were used. Dry air volume mixing ratios of CO2 and CH4 were retrieved from the ground-based observations. A FTS with a spectral resolution of 0.1 cm-1, operating between 2000 and 15000 cm-1, is suggested as the primary instrument for the mission. Further progress in improving the atmospheric retrievals for CO2, CH4 and O2 requires new laboratory measurements to improve the spectroscopic line parameters. Atmospheric observations were made with three FTSs at the Polar Environment Atmospheric Research Laboratory (PEARL) during spring 2006. The vertical column densities of O3, HCl, HNO3, HF, NO2, ClONO2 and NO from PARIS-IR, the Eureka DA8 FTS, and the ACE-FTS show good agreement. Chorine activation and denitrification in the Arctic atmosphere were observed in the extremely cold stratosphere near Eureka, Nunavut, Canada. The observed ozone depletion during the 2006 campaign was attributed to chemical removal.

A linear periodically time-varying (LPTV) system is a linear time-varying system with the coefficients changing periodically, which is widely used in control, communications, signal processing, and even circuit modeling. This thesis concentrates on identification of LPTV systems. To this end, the representations of LPTV systems are thoroughly reviewed. Identification methods are developed accordingly. The usefulness of the proposed identification methods is verified by the simulation results.<p> A periodic input signal is applied to a finite impulse response (FIR)-LPTV system and measure the noise-contaminated output. Using such periodic inputs, we show that we can formulate the problem of identification of LPTV systems in the frequency domain. With the help of the discrete Fourier transform (DFT), the identification method reduces to finding the least-squares (LS) solution of a set of linear equations. A sufficient condition for the identifiability of LPTV systems is given, which can be used to find appropriate inputs for the purpose of identification.<p> In the frequency domain, we show that the input and the output can be related by using the discrete Fourier transform (DFT) and a least-squares method can be used to identify the alias components. A lower bound on the mean square error (MSE) of the estimated alias components is given for FIR-LPTV systems. The optimal training signal achieving this lower MSE bound is designed subsequently. The algorithm is extended to the identification of infinite impulse response (IIR)-LPTV systems as well. Simulation results show the accuracy of the estimation and the efficiency of the optimal training signal design.

The application of a hollow waveguide (HW) was investigated as a gas cell for analytical infrared analysis. The analysis was the measurement of carbon monoxide (CO) and nitric oxide (NO) in sidestream cigarette smoke. An FT-IR analysis system was setup with a 3m multi-pass gas cell and a 55cm by 2mm i.d. Ag/AgI coated HW in tandem with individual CO and NO gas analyzers. The HW demonstrated response times an order of magnitude less than the larger volume multi-pass gas cell and slightly faster than the single analyte gas analyzer. Furthermore, it has been demonstrated that the HW provides up to approx. 60% greater sensitivity on a per meter optical path basis than the multi-pass gas cell of the analytes investigated due to increased optical efficiency maximizing the light concentration within the gaseous sample volume. Simulations in 3-D showed the sensitivity could theoretically improve by more than an order of magnitude if the IR beam was coupled more efficiently into the waveguide. Both FT-IR configurations gave statistically equivalent results for CO to the independent analyzers. With the HW increased temporal resolution, inter-puff measurements comparable to the gas analyzer were achieved at a lower spectral resolution. The HW optical configuration was modeled for ray tracing in MATLAB. Simulations in 2-D and 3-D were accomplished. The simulations show a major drawback to HW optimization is the coupling of the infrared beam into the waveguide. As demonstrated in a 3-D simulation, approximately 97% of the rays are rejected when an off-axis parabolic mirror with 25.4mm focal length is used to focus the IR beam into the 2mm i.d. waveguide. Repeating the simulation with longer focal length mirrors showed improved in IR coupling into the waveguide from 3% to 85%. Simulations applying a compound parabolic concentrator show comparable performance to the traditional design of two OAP mirrors to collect rays from the HW and focus onto the detector, but in a much smaller configuration. The simulation routines can be used to further improve the design of this and other optical sensing systems and enhanced by incorporating a spectral component to the simulation.

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