Thesis (M.S.)--University of Wisconsin--Madison, 1981. / Typescript. eContent provider-neutral record in process. Description based on print version record. Includes chiefly bibliographical references.

This thesis describes the design of a digital waveform synthesizer based on the Walsh series representation of a signal. By designing the unit to operate serially, simplicity and economy have been achieved. Although basically meant to be used as a speech synthesizer to be interfaced to a computer, the unit can operate independently as a low frequency function generator capable of producing essentially any finite waveform having a frequency from zero to 200Hz. The mathematics behind the Walsh Series is developed and parameters are adjusted to suit speech synthesis by a short investigation ot the properties of speech. Evolution of the hardware design, including detailed analysis of the final circuitry, is also given. Sources of error are investigated and compared to error measurements made from basic waveforms generated by the synthesizer. Finally, a discussion of potential uses of the synthesizer is included. / <p>This thesis describes the design of a digital waveform synthesizer based on signal representation by the Walsh series. The evolution of the machine design is given, along with a short error analysis. The instrument was constructed and preliminary measurements indicate output waveforms well within the bounds given by error analysis. </p> / Thesis / Master of Engineering (ME)

Due to their binary nature, the Walsh functions have considerable advantages over the traditional sinusoidal functions used in Fourier analysis when the computations are carried out by a general purpose binary digital computer. The important properties of the Walsh functions which illustrate these advantages are examined and developed. The Walsh transform and spectrum are presented in relation to the problem of function approximation, and various computational procedures for effecting the transform are explained. The unconventional 'logical' transform is developed from the Walsh transform, and there is a discussion on the subject of interpreting the resulting spectrum. There are other functions, such as the Haar functions, which are closely related to the Walsh functions, and their advantages are indicated. The process of shape analysis is dealt with in terms of its relation to the more widely treated problem of pattern recognition. An application of shape analysis, using Walsh functions, to a study of leaf shapes is illustrated by experimental results. A completely different approach to shape analysis is taken in the chapter on Pattern Generation and Simulation of Growth Processes. Other applications of Walsh functions, particularly of the 'logical' transform, are discussed in the final chapter. Throughout, tested computer programs are used to provide examples, back up conjectures, and generally illustrate numerous points in the text.

published_or_final_version / Statistics / Master / Master of Philosophy

Thesis (M. Phil.)--University of Hong Kong, 1994. / Includes bibliographical references (leaves 135-138).

International Telemetering Conference Proceedings / October 17-20, 1994 / Town & Country Hotel and Conference Center, San Diego, California / In this paper, by using computer simulations, the interference of channel data in the SDM telemetry system is investigated, the performance of the copy demultiplexing is examined, and finally the selection rule of Walsh functions is recommended.

This dissertation is devoted to theories of processes we call ``Walsh semimartingales" and ``Walsh diffusions", as well as to related optimization problems of control and stopping. These processes move on the plane along rays emanating from the origin; and when at the origin, the processes choose the rays of their subsequent voyage according to a fixed probability measure---in a manner described by Walsh (1978) as a direct generalization of the skew Brownian motion. We first review in Chapter 1 some key results regarding the celebrated skew Brownian motions and Walsh Brownian motions. These results include the characterization of skew Brownian motions via stochastic equations in Harrison & Shepp (1981), the construction of Walsh Brownian motions in Barlow, Pitman & Yor (1989), and the important result of Tsirel'son (1997) regarding the nature of the filtration generated by the Walsh Brownian motion. Various generalizations of Walsh Brownian motions are described in detail in Chapter 2. We formally define there Walsh semimartingales as a subclass of planar processes we call ``semimartingales on rays". We derive for such processes Freidlin-Sheu-type change-of-variable formulas, as well as two-dimensional versions of the Harrison-Shepp equations. The actual construction of Walsh semimartingales is given next. Walsh diffusions are then defined as a subclass of Walsh semimartingales, described by stochastic equations which involve local drift and dispersion characteristics. The associated local submartingale problems, strong Markov properties, existence, uniqueness, asymptotic behavior, and tests for explosions in finite time, are studied in turn. Finally, with Walsh semimartingales as state-processes, we study in Chapter 3 succesively a pure optimal stopping problem, a stochastic control problem with discretionary stopping, and a stochastic game between a controller and a stopper. We derive for these problems optimal strategies in surprisingly explicit from. Crucial for the analysis underpinning these results, are the change-of-variable formulas derived in Chapter 2. Most of the results in Chapters 2 and 3 are based on two papers, [21] and [31], both cowritten by the author of this dissertation. Some results and proofs are rearranged and rewritten here.

Thesis (M.S. in Engineering Science)--Naval Postgraduate School, December 1990. / Thesis Advisor(s): Davis, David S. Second Reader: Walters, D.L. "December 1990." Description based on title screen as viewed on April 1, 2010. DTIC Identifier(s): Infrared Images, Multiplexing, Spectroscopy, Applied Mathematics. Author(s) subject terms: Spectroscopy, Walsh Functions, Sequency Theory, Infrared Imaging. Includes bibliographical references (p. 120-121). Also available in print.

Thesis (M.S.)--Rochester Institute of Technology, 1994. / Typescript. Bibliography: leaves 57-58.

Orientador: Sergio Antonio Tozoni / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Cientifica / Made available in DSpace on 2018-08-18T00:43:47Z (GMT). No. of bitstreams: 1 Milare_GustavoHenrique_M.pdf: 1460238 bytes, checksum: e2c396949947fc2e7544f1c3b4a007fc (MD5) Previous issue date: 2011 / Resumo: As funções de Walsh formam um conjunto ortonormal completo de L2 [0; 1) que pode ser aplicado em diferentes situações tais como transmissão de dados, filtração, enriquecimento de imagem, análise de sinais e reconhecimento de padrão. Inicialmente estudamos alguns resultados básicos da Teoria dos Martingais, tais como a convergência de martingais, a Desigualdade de Doob e estimativas para a norma Lp da função quadrática associada a um martingal. Em seguida, estes resultados são usados no estudo da convergência das séries de Walsh em Lp e em um teorema de multiplicadores de séries de Walsh com a condição de Marcinkiewicz. Os resultados principais estudados nesta dissertação são estimativas de ordem de crescimento de entropia de operadores multiplicadores de séries de Walsh limitados de Lp em Lq / Abstract: The Walsh functions form a complete orthonormal set of functions of L2 [0; 1) which can be applied in different situations such as data transmission, filtering, image enhancement, signal analysis and patern recognition. Initially we study some basic results of the Theory of martingales, such as the convergence of martingales, Doob's inequality and estimatives for the Lp norm of the quadratic function associated to a martingale. Later, these results are used in the study of the convergence of the Walsh series in Lp and in a theorem of multipliers of Walsh series with Marcinkiewicz condition. The main results studied in this dissertation are estimatives of order of growth of entropy of limited multiplier operators of Walsh series from Lp to Lq / Mestrado / Analise / Mestre em Matemática