Στα πλαίσια της διπλωματικής εργασίας αναπτύχθηκε μία εφαρμογή, η οποία προσδιορίζει τις τρεις πρώτες συχνότητες συντονισμού της φωνητικής κοιλότητας κατά τη διαδικασία της φώνησης φωνηέντων. Οι τρεις αυτές συχνότητες παρέχουν επαρκή πληροφορία για τον προσδιορισμό του φωνήεντου. Η φώνηση εξομοιώνεται με σήμα εισόδου το οποίο παρουσιάζει κορυφές σε αναμενόμενες περιοχές συχνοτήτων. Ο προσδιορισμός των συχνοτήτων συντονισμού στηρίζεται στη μέθοδο βραχύχρονης ανάλυσης Fourier. Η εφαρμογή αναπτύχθηκε σε περιβάλλον μVision της Keil, σε γλώσσα προγραμματισμού C, για τον μικροελεγκτή STM32F103RB της ST Microelectronics. / In the context of this thesis an application was developed, that is capable of estimating the first three formant frequencies (resonances of the vocal tract) in the event of voicing of vowels. These three frequencies provide us enough information to determine the vowel that is voiced. The human voice is being emulated by an input signal which has peaks in the anticipated frequency regions. The formant frequencies are being estimated based on the short-time Fourier analysis method. The application was developed in Keil μVision programming suite, in C programming language, for the STM32F103RB microcontroller by ST Microelectronics.

Le sujet de cette thèse est le développement de méthodes itératives permettant la résolution degrands systèmes linéaires creux d'équations présentant plusieurs seconds membres simultanément. Ces méthodes seront en particulier utilisées dans le cadre d'une application géophysique : la migration sismique visant à simuler la propagation d'ondes sous la surface de la terre. Le problème prend la forme d'une équation d'Helmholtz dans le domaine fréquentiel en trois dimensions, discrétisée par des différences finies et donnant lieu à un système linéaire creux, complexe, non-symétrique, non-hermitien. De plus, lorsque de grands nombres d'onde sont considérés, cette matrice possède une taille élevée et est indéfinie. Du fait de ces propriétés, nous nous proposons d'étudier des méthodes de Krylov préconditionnées par des techniques hiérarchiques deux niveaux. Un tel pre-conditionnement s'est montré particulièrement efficace en deux dimensions et le but de cette thèse est de relever le défi de l'adapter au cas tridimensionel. Pour ce faire, des méthodes de Krylov sont utilisées à la fois comme lisseur et comme méthode de résolution du problème grossier. Ces derniers choix induisent l'emploi de méthodes de Krylov dites flexibles. / The topic of this PhD thesis is the development of iterative methods for the solution of large sparse linear systems of equations with possibly multiple right-hand sides given at once. These methods will be used for a specific application in geophysics - seismic migration - related to the simulation of wave propagation in the subsurface of the Earth. Here the three-dimensional Helmholtz equation written in the frequency domain is considered. The finite difference discretization of the Helmholtz equation with the Perfect Matched Layer formulation produces, when high frequencies are considered, a complex linear system which is large, non-symmetric, non-Hermitian, indefinite and sparse. Thus we propose to study preconditioned flexible Krylov subspace methods, especially minimum residual norm methods, to solve this class of problems. As a preconditioner we consider multi-level techniques and especially focus on a two-level method. This twolevel preconditioner has shown efficient for two-dimensional applications and the purpose of this thesis is to extend this to the challenging three-dimensional case. This leads us to propose and analyze a perturbed two-level preconditioner for a flexible Krylov subspace method, where Krylov methods are used both as smoother and as approximate coarse grid solver.

Time Average Fourier Telescopy (TAFT) has been proposed as a means for obtaining high-resolution, diffraction-limited images over large distances through ground-level horizontal-path atmospheric turbulence. Image data is collected in the spatial-frequency, or Fourier, domain by means of Fourier Telescopy; an inverse two dimensional Fourier transform yields the actual image. TAFT requires active illumination of the distant object by moving interference fringe patterns. Light reflected from the object is collected by a “light-bucket” detector, and the resulting electrical signal is digitized and subjected to a series of signal processing operations, including an all-critical averaging of the amplitude and phase of a number of narrow-band signals. / Includes bibliography. / Dissertation (Ph.D.)--Florida Atlantic University, 2014. / FAU Electronic Theses and Dissertations Collection

Inlet flow distortion is a non-uniform total pressure, total temperature, or swirl (flow angularity) condition at an aircraft engine inlet. Inlet distortion is a critical consideration in modern fan and compressor design. This is especially true as the industry continues to increase the efficiency and operating range of air breathing gas turbine engines. The focus of this paper is to evaluate the Computational Fluid Dynamics (CFD) Harmonic Balance (HB) solver in STAR-CCM+ as a reduced order method for capturing inlet distortion as well as the associated distortion transfer and generation. New methods for quantitatively describing and analyzing distortion transfer and generation are investigated. The geometry used is the rotor 4 fan geometry, consisting of one rotor and one stator. The inlet boundary condition is a 90-degree sector total pressure distortion profile with total pressure and swirl held constant. Multiple HB simulations with varying mode combinations and distortion intensities are analyzed and compared against full annulus Unsteady Reynolds Averaged Navier-Stokes (URANS) simulations. Best practices and recommendations for the implementation of the HB solver are given. The pre-existing Society of Automotive Engineers Aerospace Recommended Practice (SAE-ARP) 1420b descriptors are demonstrated to be inadequate for the purposes of analyzing distortion transfer and generation on a stage-to-stage basis. New implementations of Fourier methods are presented as an alternative to the SAE-ARP 1420b descriptors. These Fourier descriptors are shown to describe distortion transfer and generation to a higher degree of fidelity than the SAE-ARP 1420b descriptors. These new descriptors are demonstrated on the analysis of full annulus URANS and HB simulations. The HB solver is shown to be capable of capturing distortion transfer, generation and performance degradation. Recommendations for the optimal implementation of the HB method are given.

This thesis treats two essentially different subjects: V-cycle schemes are considered in Chapters 2-4, whereas the aggregation-based coarsening is analysed in Chapters 5-6. As a matter of paradox, these two multigrid ingredients, when combined together, can hardly lead to an optimal algorithm. Indeed, a V-cycle needs more accurate prolongations than the simple piecewise-constant one, associated to aggregation-based coarsening. On the other hand, aggregation-based approaches use almost exclusively piecewise constant prolongations, and therefore need more involved cycling strategies, K-cycle <a href=http://www3.interscience.wiley.com/journal/114286660/abstract?CRETRY=1&SRETRY=0>[Num.Lin.Alg.Appl., vol.15(2008), pp.473-487]</a> being an attractive alternative in this respect. <br> <br> Chapter 2 considers more precisely the well-known V-cycle convergence theories: the approximation property based analyses by Hackbusch (see [Multi-Grid Methods and Applications, 1985, pp.164-167]) and by McCormick [SIAM J.Numer.Anal., vol.22(1985), pp.634-643] and the successive subspace correction theory, as presented in [SIAM Review, vol.34(1992), pp.581-613] by Xu and in [Acta Numerica, vol.2(1993), pp.285-326.] by Yserentant. Under the constraint that the resulting upper bound on the convergence rate must be expressed with respect to parameters involving two successive levels at a time, these theories are compared. Unlike [Acta Numerica, vol.2(1993), pp.285-326.], where the comparison is performed on the basis of underlying assumptions in a particular PDE context, we compare directly the upper bounds. We show that these analyses are equivalent from the qualitative point of view. From the quantitative point of view, we show that the bound due to McCormick is always the best one. <br> <br> When the upper bound on the V-cycle convergence factor involves only two successive levels at a time, it can further be compared with the two-level convergence factor. Such comparison is performed in Chapter 3, showing that a nice two-grid convergence (at every level) leads to an optimal McCormick's bound (the best bound from the previous chapter) if and only if a norm of a given projector is bounded on every level. <br> <br> In Chapter 4 we consider the Fourier analysis setting for scalar PDEs and extend the comparison between two-grid and V-cycle multigrid methods to the smoothing factor. In particular, a two-sided bound involving the smoothing factor is obtained that defines an interval containing both the two-grid and V-cycle convergence rates. This interval is narrow when an additional parameter α is small enough, this latter being a simple function of Fourier components. <br> <br> Chapter 5 provides a theoretical framework for coarsening by aggregation. An upper bound is presented that relates the two-grid convergence factor with local quantities, each being related to a particular aggregate. The bound is shown to be asymptotically sharp for a large class of elliptic boundary value problems, including problems with anisotropic and discontinuous coefficients. <br> <br> In Chapter 6 we consider problems resulting from the discretization with edge finite elements of 3D curl-curl equation. The variables in such discretization are associated with edges. We investigate the performance of the Reitzinger and Schöberl algorithm [Num.Lin.Alg.Appl., vol.9(2002), pp.223-238], which uses aggregation techniques to construct the edge prolongation matrix. More precisely, we perform a Fourier analysis of the method in two-grid setting, showing its optimality. The analysis is supplemented with some numerical investigations.

This thesis consists of five articles and a summary. Thethesis deals with methods for measuring properties of thevoice. The methods are all computer-based, but utilisedifferent approaches for measuring different aspects of thevoice. Paper I introduces the Visual Sort and Rate (VSR) method forperceptual rating of voice quality. The method is based on theVisual Analogue Scale (VAS), but simultaneously shows allstimuli as icons along the VAS on the computer screen. As thelistener places similar-sounding stimuli close to each otherduring the rating process, comparing stimuli becomeseasier. Paper II introduces the correlogram. Fundamental frequencyF0 sometimes cannot be strictly defined, particularly forperturbed voice signals. The method displays multipleconsecutive correlation functions in a grey scale image. Thus,the correlogram avoids selecting a single F0 value. Rather itpresents an unbiased image of periodicity, allowing theinvestigator to select among several candidates, ifappropriate. PaperIII introduces a method for detection of phonation tobe utilised in voice accumulators. The method uses twomicrophones attached near the subject’s ears. Phase andamplitude relations of the microphone signals are used to forma phonation detector. The output of the method can be used tomeasure phonation time, speaking time and fundamental frequencyof the subject, as well as sound pressure level of both thesubject’s voicing and the ambient sounds. Paper IV introduces a method for Fourier analysis ofhigh-speed laryngoscopic imaging. The data from the consecutiveimages are re-arranged to form time-series that reflect thetime-variation of light intensity in each pixel. Each of thesetime series is then analysed by means of Fouriertransformation, such that a spectrum for each pixel isobtained. Several ways of displaying these spectra aredemonstrated. Paper V examines a test set-up for simultaneous recording ofairflow, intra-oral pressure, electro-glottography, audio andhigh-speed imaging. Data are analysed with particular focus onsynchronisation between glottal area and inverse filteredairflow. Several methodological aspects are also examined, suchas the difficulties in synchronising high-speed imaging datawith the other signals. / QC 20100609

University of Macau / Faculty of Science and Technology / Department of Mathematics

University of Macau / Faculty of Science and Technology / Department of Mathematics

The objective of the present study is to forecast annual rainfall taking into account the periodicities and structure of the stochastic component. This study has six Chapters. Chapter 1 presents introduction to the problem and objectives of the study. Chapter 2 consists of review of literature. Chapter 3 deals with the model formulation and development. Chapter 4 gives an account of the application of the model. Chapter 5 presents results and discussions. Chapter 6 gives the conclusions drawn from the study. In this thesis the following model formulations are presented in order to achieve the objective. Fourier analysis model is used to identify periodicities that are present in the rainfall series.1 These periodic components are used to obtain discrotized ranges which is an essential input for the Fourier series model. Auto power regression model is developed for estimation of rainfall and hence to compute the first order residuals errlt The parameters of the model are estimated using genetic algorithm. The auto power regression model is of the form, ( Refer the PDF File for Formula) where αi and βi are parameters and M indicates modular value. Fourier series model is formulated and solved through genetic algorithm to estimate the parameters amplitude R, phase Φ and periodic frequency wj for the residual series errlt. The ranges for the parameters R, Φ and wj were obtained from Fourier analysis model. errl't= /µerrlt+ Σj Rcos(wjt+ Φ) Further, an integrated auto power regression and Fourier series model developed (with parameters of the model being known from the above analysis) to estimate new rainfall series Zesťt=Zµ Σ t αi(ZMi-t ) βi+µerrl+ Σj Rcos(wjt+ Φ) and the second order residuals, err2t is computed using, err2t = (zt –Zesťt) Thus, the periodicities are removed in the errlt series and the second order residuals err'2f obtained represents the stochastic component of the actual rainfall series. Auto regressive model is formulated to study the structure of the stochastic component err2t. The auto regressive model of order two AR(2) is found to fit well. The parameters of the AR(2) model were estimated using method of least squares. An exponential weighting function is developed to compute the weight considering weight as a function of AR{2) parameters. The product of weight and Gaussian white noise N(0, óerr2) is termed as weighted stochastic component. Also, drought analysis is performed considering annual (January to December) and summer monsoon (June to September) rainfall totals, to determine average drought interval (idrt) which is used in assigning signs to the random component of the forecasting model. In the final form of the forecasting model. Zest”t = Z µ Σ t αi(ZMi-t ) βi+µerrl+ Σj Rcos(wjt+ Φ) ± WT(Φ1, Φ2)N(0, óerr2) The weighted stochastic component is added or subtracted considering two criteria. Criterion I is used for all rainfall series except all-India series for which criterion II is used. The criteria also consider average drought interval Further, it can be seen that a ± sign is introduced to add or subtract the weighted stochastic component, albeit the stochastic component itself can either be positive or negative. The introduction of ± sign on the already signed value (instead of absolute value) is found to improve the forecast in the sense of obtaining more number of point rainfall estimates within 20 percent error. Incorporating significant periodicities, and weighted stochastic component along with average drought interval into the forecasting formulation is the main feature of the model. Thus, in the process of rainfall prediction, the genetic algorithm is used as an efficient tool in estimating optimal parameters of the auto power regression and the Fourier series models, without the use of an expensive nonlinear least square algorithm. The model application is demonstrated considering different annual rainfall series relating to IMD-Regions (RI...R5), all-india (AI), IMD-Subdivisions (S1...S29), Zones (Z1...Z10) and all-Karnataka (AK). The results of the proposed model are encouraging in providing improved forecasts. The model considers periodicity, average critical drought frequency and weighted stochastic component in forecasting the rainfall series. The model performed well in achieving success-rate of 70 percent with percentage error less than 20 percent in 4 out of 5 IMD Regions (R2 to R5), all-India, 17 out of 29 IMD Subdivisions (S1 to S5, S7 to S9, S18, S19, S21, S24 to S29) and all-Karnataka rainfall series. The model performance for Zones was not that-satisfactory as only 2 out of 10 Zones [Z1 and Z2) met the criterion. In a separate study, an effort was made to forecast annual rainfall using IMSL subroutine SPWF -which estimates Wiener forecast parameters. Monthly data is considered for the study. The Wiener parameters obtained were used to estimate monthly rainfall. The annual estimates obtained by simple aggregation of the monthly estimates compared extremely well with the actual annual rainfall values. A success rate of more than 80 percent with percentage error less than 10 percent is achieved in 4 out of 5 IMD Regions (R2 to R5), all-India, 18 out of 29 IMD Subdivisions (S1 to S8, S14, S18, S19, S22 to S24, S26 to S29) and all-Karnataka rainfall series. Whereas a success rate of 80 percent within 20 percent error is achieved in 4 out of 5 IMD Regions (except R1), all-India, 25 outof 29 IMD Subdivisions (except S10, S11, S12 and S17), all- Karnataka and 8 out of 10 Zones (except Z6 and Z8)(Please refer PDF File for Formulas)

Solar radiation is a primary driving force behind a number of solar energy applications such as photovoltaic systems for electricity generation amongst others. Hence, the accurate modelling and prediction of the solar flux incident at a particular location, is essential for the design and performance prediction of solar energy conversion systems. In this regard, literature shows that time series models such as the Box-Jenkins Seasonal/Non-seasonal Autoregressive Integrated Moving Average (S/ARIMA) stochastic models have considerable efficacy to describe, monitor and forecast solar radiation data series at various sites on the earths surface (see e.g. Reikard, 2009). This success is attributable to their ability to capture the stochastic component of the irradiance series due to the effects of the ever-changing atmospheric conditions. On the other hand at the top of the atmosphere, there are no such conditions and deterministic models which have been used successfully to model extra-terrestrial solar radiation. One such modelling procedure is the use of a sinusoidal predictor at determined harmonic (Fourier) frequencies to capture the inherent periodicities (seasonalities) due to the diurnal cycle. We combine this deterministic model component and SARIMA models to construct harmonically coupled SARIMA (HCSARIMA) models to model the resulting mixture of stochastic and deterministic components of solar radiation recorded at the earths surface. A comparative study of these two classes of models is undertaken for the horizontal global solar irradiance incident on the solar panels at UKZN Howard College (UKZN HC), located at 29.9º South, 30.98º East with elevation, 151.3m. The results indicated that both SARIMA and HCSARIMA models are good in describing the underlying data generating processes for all data series with respect to different diagnostics. In terms of the predictive ability, the HCSARIMA models generally had a competitive edge over the SARIMA models in most cases. Also, a tentative study of long range dependence (long memory) shows this phenomenon to be inherent in high frequency data series. Therefore autoregressive fractionally integrated moving average (ARFIMA) models are recommended for further studies on high frequency irradiance. / M.Sc. University of KwaZulu-Natal, Durban 2014.