A reproducing kernel Hilbert space (RKHS) is a Hilbert space $\mathscr{H}$ of functions with the property that the values $f(x)$ for $f \in \mathscr{H}$ are reproduced from the inner product in $\mathscr{H}$. Recent applications are found in stochastic processes (Ito Calculus), harmonic analysis, complex analysis, learning theory, and machine learning algorithms. This research began with the study of RKHSs to areas such as learning theory, sampling theory, and harmonic analysis. From the Moore-Aronszajn theorem, we have an explicit correspondence between reproducing kernel Hilbert spaces (RKHS) and reproducing kernel functions—also called positive definite kernels or positive definite functions. The focus here is on the duality between positive definite functions and their boundary spaces; these boundary spaces often lead to the study of Gaussian processes or Brownian motion. It is known that every reproducing kernel Hilbert space has an associated generalized boundary probability space. The Arveson (reproducing) kernel is $K(z,w) = \frac{1}{1-_{\C^d}}, z,w \in \B_d$, and Arveson showed, \cite{Arveson}, that the Arveson kernel does not follow the boundary analysis we were finding in other RKHS. Thus, we were led to define a new reproducing kernel on the unit ball in complex $n$-space, and naturally this lead to the study of a new reproducing kernel Hilbert space. This reproducing kernel Hilbert space stems from boundary analysis of the Arveson kernel. The construction of the new RKHS resolves the problem we faced while researching “natural” boundary spaces (for the Drury-Arveson RKHS) that yield boundary factorizations: \[K(z,w) = \int_{\mathcal{B}} K^{\mathcal{B}}_z(b)\overline{K^{\mathcal{B}}_w(b)}d\mu(b), \;\;\; z,w \in \B_d \text{ and } b \in \mathcal{B} \tag*{\it{(Factorization of} $K$).}\] Results from classical harmonic analysis on the disk (the Hardy space) are generalized and extended to the new RKHS. Particularly, our main theorem proves that, relaxing the criteria to the contractive property, we can do the generalization that Arveson's paper showed (criteria being an isometry) is not possible.

Thesis (M.Phil.)--University of Stellenbosch, 2004. / ENGLISH ABSTRACT: Sound sample libraries represent the format in which huge collections of sampled sounds are made available for use within digital samplers and/or other digital audio workstations (DAW’s). Although in use for many years, little or no academic research has been done on the methodology of compiling a commercial sound sample library. In this endeavour, the factors influencing the design, recording and publishing of a sound sample library are investigated through the actual design of a drum sample library. The rationale behind the sampling of a drum kit is carefully depicted in the light of various other factors influencing the instrument, as well as being influenced by the instrument itself. A professional drummer was engaged to play a state-of-the art Gretsch acoustic drum kit. Samples of the kit, consisting of various individual instrument parts, were recorded in three locations within the Konservatorium of Stellenbosch University, for reasons carefully explained in the text. These numerous drum hits were mixed and cut into individual drum samples. The samples were mapped into a digital software sampler, GigaStudio, creating five distinct collections of drum samples that faithfully represent the quality of the drum kit, the recording rooms as well as the equipment used in the process. The outcome of the study is a professional product in the form of a Gretsch drum sample collection, prepared for commercial release. Many of the drum samples have already been used successfully in commercial music releases over the past 12 months. Whilst the drum sample library is currently being published, the product and documentation clearly depict the viability of the study in terms of the artistic and academic expectations that have been met. The study anticipates future research on the subject. / AFRIKAANSE OPSOMMING: Klankbiblioteke heet die formaat waarin versamelings van klankmonsters beskikbaar gestel word vir gebruik in digitale samplers1 en/of ander digitale klankprogrammatuur. Nieteenstaande die feit dat klankbiblioteke reeds jare in gebruik is, is geen studie waarin die ontwerp en saamstel van so ‘n biblioteek beskryf word, bekend nie. In hierdie navorsingsprojek word die faktore wat die ontwerp, opneem en vrystelling van ‘n klankbiblioteek beïnvloed bestudeer deur die skep van so ‘n biblioteek. Die oorwegings vir die keuse van ‘n tromstel is noukeurig uiteengesit in die lig van die faktore wat betrekking het tot, en wederkerig beïnvloed is deur die instrument en opname-omgewing. ‘n Professionele tromspeler is vir die projekdoeleindes gekontrakteer om ‘n Gretsch akoestiese tromstel te speel. Klankmonsters van die tromstel se individuele komponente is in drie lokale binne die Konservatorium van die Universiteit van Stellenbosch opgeneem, met redes soos uiteengestip in die teks. Klankopnames van die talle tromslae is gemeng en opgesny in individuele klankmonsters. Laasgenoemde is in GigaStudio, ‘n digitale sagteware sampler, gekarteer sodat vyf duidelik-onderskeibare klankveramelings geskep is. Hierdie versamelings lig die kwaliteit van die tromstel asook die verskeie opnamelokale en toerusting wat gebruik is duidelik uit. Die resultaat van die studie is ‘n professionele produk in die vorm van ‘n Gretsch kommersiële klankbiblioteek, waarvan verskeie klankmonsters reeds oor die afgelope 12 maande in plaaslike musiekvrystellings gebruik is. Hoewel die klankbiblioteek huidiglik vrygestel word, toon die produk en dokumentasie duidelik die artistiese en tegniese waardigheid van die studie. Die studie antisipeer toekomstige navorsings-moontlikhede wat uit die onderwerp mag voortspruit.

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A thesis submitted to the Faculty of Humanities, University of the Witwatersrand, Johannesburg, in fulfilment of the requirements for the Degree of Master of Music Johannesburg 2016 / Recently, scholarly work in the field of film sound design has emphasised the crucial significance of sound in film. Writers such as Mark Underwood (2008), Larry Sider (2003) and Danijela Kulezic-Wilson (2008) have expressed the view that film sound design ought to be approached from a musical perspective substantiating this position through analytical discussions on the relatively musical use of sound design in scenes from films such as Alfred Hitchcock’s The Birds (1963) and Darren Aronofsky’s Requiem for a Dream (2000). Building upon the work of these and other scholars, this thesis investigates the varying ways in which music and foley sound design relate and interact within a film seeking to categorise with some specificity the various ways in which foley sound design can ascend beyond its ordinary remit and in so doing function in lieu of film music as well as in cooperation with it. I consider examples from, amongst others, The Godfather, parts one (1972) and two (1974) by Francis Ford Coppola and The Matrix (1999) by Ana and Lana Wachowski. In each chapter of part one of the thesis (which I call Take 1), I explore a particular aspect of the way in which foley makes known its capacity to function quasi-musically. Chapter one looks at Walter Murch’s concept of the metaphoric use of sound and how, through this technique, foley sound can be applied so as to fulfil roles more accustomed to film music in its stead. Chapter two details some of the ways in which film music and foley interact within a film. A crucial element of this discussion is the on going debate between scholars such as Michel Chion who disavow the existence of a soundtrack and others such as Rick Altman who contradict Chion on this matter. Chapter three looks at how otherworldly diegetic contexts help to encourage creativity in designing and applying foley sounds so as to further enhance its pre-discussed ability to act in film music’s stead while chapter four focuses on the voice as the soloist within the melee of sounds that constitute the film soundtrack. Part two (or Take 2) of the thesis consists of compositions written in response to some of the theories and concepts explored in the first part of the thesis including a ‘dramatic string quartet’ in which I attempt to realise in a musical composition some of the ideas discussed in all four of the chapters. I conclude the thesis by reflecting on the main insights uncovered throughout the thesis in addition to reflecting on the process of composing the pieces in relation to the relative success of the performances thereof. / GR2017

Um espaço de Hilbert de reprodução (EHR) é um espaço de Hilbert de funções construído de maneira específica e única a partir de um núcleo positivo definido. As funções do EHR tem a seguinte peculiaridade: seus valores podem ser reproduzidos através de uma operação elementar envolvendo a própria função, o núcleo gerador e o produto interno do espaço. Neste trabalho, consideramos EHR gerados por núcleos positivos definidos sobre a esfera unitária m-dimensional usual. Analisamos quais propriedades são herdadas pelos elementos do espaço, quando o núcleo gerador possui alguma hipótese de diferenciabilidade. A análise é elaborada em duas frentes: com a noção de diferenciabilidade usual sobre a esfera e com uma noção de diferenciabilidade definida por uma operação multiplicativa genérica. Esta última inclui como caso particular as derivadas fracionárias e a derivada forte de Laplace-Beltrami. Em cada um dos casos consideramos ainda propriedades específicas do mergulho do EHR em espaços de funções suaves definidos pela diferenciabilidade utilizada / A reproducing kernel Hilbert space (EHR) is a Hilbert space of functions constructed in a unique manner from a fixed positive definite generating kernel. The values of a function in a reproducing kernel Hilbert space can be reproduced through an elementary operation involving the function itself, the generating kernel and the inner product of the space. In this work, we consider reproducing kernel Hilbert spaces generated by a positive definite kernel on the usual m-dimensional sphere. The main goal is to analyze differentiability properties inherited by the functions in the space when the generating kernel carries a differentiability assumption. That is done in two different cases: using the usual notion of differentiability on the sphere and using another one defined through multiplicative operators. The second case includes the Laplace-Beltrami derivative and fractional derivatives as well. In both cases we consider specific properties of the embeddings of the reproducing kernel Hilbert space into spaces of smooth functions induced by notion of differentiability used

O estudo teve por objetivo mostrar que as formas de relevo observadas na Bacia do Piracicamirim/SP traduzem a dependência genética de todo o conjunto de estruturas que se articulam no geossistema paisagístico dessa unidade geográfica, tendo por isso, grande importância como indicadoras da dinâmica precedente e da situação atual do mesmo, razão pela qual, o seu estudo foi tomado como fundamental não só para explicar a evolução dos processos geoecológicos da área mas, também, como norteador e, portanto, subsídio para o (re) planejamento futuro da referida bacia. A escolha da bacia em questão se justifica por sua meso-escala, o que a coloca, metodologicamente como adequada, para estudos de tendências, padrões de comportamento e de processos. A elaboração da carta morfodinâmica como método da pesquisa decorreu da intenção de avaliar a participação relativa do relevo na dinâmica dos processos, bem como da meta de identificar os graus de fragilidade ambiental. O estudo comprovou que a dinâmica das formas de relevo e as propriedades adquiridas em sua gênese determinaram a evolução dos processos geoecológicos e sócio-reprodutores observados na área; reforçou a adequação da perspectiva sistêmica e da sua materialização em uma carta síntese para estudos geomorfológicos com a pretensão técnica de subsidiar planejamento territorial; comprovou os riscos decorrentes da adoção, para o estudo de realidades complexas, de procedimentos exclusivamente analíticos; disponibilizou elementos de crítica em relação a procedimentos empíricos e computacionais de cartografação geomorfológica; identificou a relação relevo/solo/uso da terra como a que principalmente está a responder pela fragilidade ambiental na bacia; disponibilizou o ferramental que poderá subsidiar as necessárias ações públicas de (re) planejamento urbano/rural e de educação ambiental da área. / This study had the objective of showing that the shapes of the relief seen in the Piracicamirim Basin/SP translate the genetic dependence of all set of structures that articulate themselves in the geosystem of the landscape of this geographic unit, having thus great importance as indicators of the precedent dynamic and of its actual situation, this been the reason why its study was taken as fundamental not only to explain the evolution of the area geoecological processes but also as a north, and therefore a subside to the future (re)planning of the referred basin. The choice of this particular basin justifies itself for its meso-scale, which places itself methodologically as adequate to the studies of tendencies, processes and behavioral standards. The elaboration of the morphodynamic chart as methodology of research resulted from the intention of evaluating the relative participation of the relief in the dynamic of the processes as well as of the goal of identifying the levels of environmental fragility.The study proved that the dynamic of the shapes of relief and the acquired properties in their genesis determined the evolution of the geoecological and social- reproducing processes seen in the area ; reinforced the adequation of the systematic perspective and its materialization in a chart synthesis to geomorphological studies with the technical intension of subsidizing territorial planning; reassured the resultant risks of the adoption, to the study of complex realities, of exclusively analytical approaches; made critic elements in relation to empiric and computational approaches of geomorphologic cartographing available; identified the relation relief/soil/use of the land like the principal one to answer to environmental fragility of the basin; made the tool that can subsidize the necessary public actions of rural/urban (re)planning and of environmental education of the area.

Um espaço de Hilbert de reprodução (EHR) é um espaço de Hilbert de funções construído de maneira específica e única a partir de um núcleo positivo definido. As funções do EHR tem a seguinte peculiaridade: seus valores podem ser reproduzidos através de uma operação elementar envolvendo a própria função, o núcleo gerador e o produto interno do espaço. Neste trabalho, consideramos EHR gerados por núcleos positivos definidos sobre a esfera unitária m-dimensional usual. Analisamos quais propriedades são herdadas pelos elementos do espaço, quando o núcleo gerador possui alguma hipótese de diferenciabilidade. A análise é elaborada em duas frentes: com a noção de diferenciabilidade usual sobre a esfera e com uma noção de diferenciabilidade definida por uma operação multiplicativa genérica. Esta última inclui como caso particular as derivadas fracionárias e a derivada forte de Laplace-Beltrami. Em cada um dos casos consideramos ainda propriedades específicas do mergulho do EHR em espaços de funções suaves definidos pela diferenciabilidade utilizada / A reproducing kernel Hilbert space (EHR) is a Hilbert space of functions constructed in a unique manner from a fixed positive definite generating kernel. The values of a function in a reproducing kernel Hilbert space can be reproduced through an elementary operation involving the function itself, the generating kernel and the inner product of the space. In this work, we consider reproducing kernel Hilbert spaces generated by a positive definite kernel on the usual m-dimensional sphere. The main goal is to analyze differentiability properties inherited by the functions in the space when the generating kernel carries a differentiability assumption. That is done in two different cases: using the usual notion of differentiability on the sphere and using another one defined through multiplicative operators. The second case includes the Laplace-Beltrami derivative and fractional derivatives as well. In both cases we consider specific properties of the embeddings of the reproducing kernel Hilbert space into spaces of smooth functions induced by notion of differentiability used

Usando o modelo de ajustamento apresentado por Schaffrin (2001), este trabalho apresenta uma metodologia para ajustamento de redes geodésicas GPS de densificação e extensão, a qual substitui com vantagem o tratamento clássico que utiliza um ajustamento livre seguido por uma \"transformação de Helmert\". A característica deste método é introduzir um procedimento estatisticamente ótimo, baseado no princípio dos mínimos quadrados, que permita ajustar a nova rede, vinculando-a a pontos fiduciais, e conectando-a a pontos de ligação com redes vizinhas de mesmo nível, considerados \"hierarquicamente superiores\" no processo. A técnica da \"propriedade reprodutora\" permite que esses pontos sejam ponderados em função das variâncias decorrentes de suas determinações, mas tenham suas coordenadas preservadas. Para a implementação dessa metodologia, foi desenvolvido um programa, em linguagem FORTRAN, que realiza o ajustamento vetorial da rede, utilizando o modelo paramétrico do método dos mínimos quadrados. O procedimento adotado consiste em fazer com que as variâncias dos pontos de injunção sejam introduzidas na nova rede, e que as coordenadas desses pontos, modificadas pelo ajustamento, sejam recuperadas. O programa apresenta também uma seqüência de testes que possibilitam a detecção, investigação e adaptação de possíveis erros encontrados. / By using the adjustment model presented by Schaffrin (2001), this work presents a methodology for the adjustment of GPS geodetic networks of densification and extension, which substitutes with advantage the classic treatment that uses a free net adjustment followed by a \"Helmert transformation\". The feature of this method is to introduce a statistically optimal procedure, based on least squares principle, that allows adjust the new network, linking it to fiducial points and connecting it to tiepoints with same level neighbor networks, all of them considered \"hierarchically superior\" in the process. The \"reproducing property\" technique allows that these points were weighed up as a function of the variances obtained in the preliminary determination, but they have their coordinates preserved. For this methodology implementation, a software in FORTRAN language was developed for the network vectorial adjustment, by using the linear parametric model of least-squares method. The adopted procedure allows the constraint point variances to propagate in the new network, but afterwards the coordinates of these points, changed in the adjustment, are retrieved. The software presents a sequence of tests to detect, to investigate and to analyze possible encountered errors, too.

This work explores the process of model-based classification of speech audio signals using low-level feature vectors. The process of extracting low-level features from audio signals is described along with a discussion of established techniques for training and testing mixture model-based classifiers and using these models in conjunction with feature selection algorithms to select optimal feature subsets. The results of a number of classification experiments using a publicly available speech database, the Berlin Database of Emotional Speech, are presented. This includes experiments in optimizing feature extraction parameters and comparing different feature selection results from over 700 candidate feature vectors for the tasks of classifying speaker gender, identity, and emotion. In the experiments, final classification accuracies of 99.5%, 98.0% and 79% were achieved for the gender, identity and emotion tasks respectively. / by Chris Thoman. / Thesis (M.S.C.S.)--Florida Atlantic University, 2009. / Includes bibliography. / Electronic reproduction. Boca Raton, Fla., 2009. Mode of access: World Wide Web.

by Tsang Yick Man, Steven. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1997. / Includes bibliographical references (leaves 94-99). / ABSTRACT --- p.i / ACKNOWLEDGMENT --- p.ii / LIST OF GLOSSARY --- p.iii / Chapter 1 --- INTRODUCTION --- p.1 / Chapter 1.1 --- What is the jitter ？ --- p.3 / Chapter 2 --- WHY DOES JITTER OCCUR IN DIGITAL AUDIO ？ --- p.4 / Chapter 2.1 --- Poorly-designed Phase Locked Loop ( PLL ) --- p.4 / Chapter 2.1.1 --- Digital data problem --- p.7 / Chapter 2.2 --- Sampling jitter or clock jitter ( Δti) --- p.9 / Chapter 2.3 --- Waveform distortion --- p.12 / Chapter 2.4 --- Logic induced jitter --- p.17 / Chapter 2.4.1 --- Digital noise mechanisms --- p.20 / Chapter 2.4.2 --- Different types of D-type flop-flip chips are linked below for ease of comparison --- p.21 / Chapter 2.4.3 --- Ground bounce --- p.22 / Chapter 2.5 --- Power supply high frequency noise --- p.23 / Chapter 2.6 --- Interface Jitter --- p.25 / Chapter 2.7 --- Cross-talk --- p.28 / Chapter 2.8 --- Inter-Symbol-Interference (ISI) --- p.28 / Chapter 2.9 --- Baseline wander --- p.29 / Chapter 2.10 --- Noise jitter --- p.30 / Chapter 2.11 --- FIFO jitter reduction chips --- p.31 / Chapter 3 --- JITTER REDUCTION TECHNIQUES --- p.33 / Chapter 3.1 --- Why using two-stage phase-locked loop (PLL ) ？ / Chapter 3.1.1 --- The PLL circuit components --- p.35 / Chapter 3.1.2 --- The PLL timing specifications --- p.36 / Chapter 3.2 --- Analog phase-locked loop (APLL ) circuit usedin second stage --- p.38 / Chapter 3.3 --- All digital phase-locked loop (ADPLL ) circuit used in second stage --- p.40 / Chapter 3.4 --- ADPLL design --- p.42 / Chapter 3.4.1 --- "Different of K counter value of ADPLL are listed for comparison with M=512, N=256, Kd=2" --- p.46 / Chapter 3.4.2 --- Computer simulated results and experimental results of the ADPLL --- p.47 / Chapter 3.4.3 --- PLL design notes --- p.58 / Chapter 3.5 --- Different of the all digital Phase-Locked Loop (ADPLL ) and the analogue Phase-Locked Loop (APLL ) are listed for comparison --- p.65 / Chapter 3.6 --- Discrete transistor oscillator --- p.68 / Chapter 3.7 --- Discrete transistor oscillator circuit operation --- p.69 / Chapter 3.8 --- The advantage and disadvantage of using external discrete oscillator --- p.71 / Chapter 3.9 --- Background of using high-precision oscillators --- p.72 / Chapter 3.9.1 --- The temperature compensated crystal circuit operation --- p.73 / Chapter 3.9.2 --- The temperature compensated circuit design notes --- p.75 / Chapter 3.10 --- The discrete voltage reference circuit operation --- p.76 / Chapter 3.10.1 --- Comparing the different types of Op-amps that can be used as a voltage comparator --- p.79 / Chapter 3.10.2 --- Precaution of separate CMOS chips Vdd and Vcc --- p.80 / Chapter 3.11 --- Board level jitter reduction method --- p.81 / Chapter 3.12 --- Digital audio interface chips --- p.82 / Chapter 3.12.1 --- Different brand of the digital interface receiver (DIR) chips and clock modular are listed for comparison --- p.84 / Chapter 4. --- APPLICATION CIRCUIT BLOCK DIAGRAMS OF JITTER REDUCTION AND CLOCK RECOVERY --- p.85 / Chapter 5 --- CONCLUSIONS --- p.90 / Chapter 5.1 --- Summary of the research --- p.90 / Chapter 5.2 --- Suggestions for further development --- p.92 / Chapter 5.3 --- Instrument listing that used in this thesis --- p.93 / Chapter 6 --- REFERENCES --- p.94 / Chapter 7 --- APPENDICES --- p.100 / Chapter 7.1.1 --- Phase instability in frequency dividers / Chapter 7.1.2 --- The effect of clock tree on Tskew on ASIC chip / Chapter 7.1.3 --- Digital audio transmission----Why jitter is important? / Chapter 7.1.4 --- Overview of digital audio interface data structures / Chapter 7.1.5 --- Typical frequency Vs temperature variations curve of Quartz crystals / Chapter 7.2 --- IC specification used in these research project