Thesis (Ph. D.)--Catholic University of America, 1941. / Includes index. "Publications of Robert Walsh": p. 229-230. "Bibliographical note": p. 231-243.

Thesis (Ph. D.)--Catholic University of America, 1941. / Includes index. "Publications of Robert Walsh": p. 229-230. "Bibliographical note": p. 231-243.

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).

Dissertação (mestrado) - Universidade Federal de Santa Catarina, Centro Tecnológico. Programa de Pós-Graduação em Engenharia Elétrica. / Made available in DSpace on 2012-10-22T12:58:31Z (GMT). No. of bitstreams: 1 234083.pdf: 4014648 bytes, checksum: ca9aba14dc03d197a335d5be935d9af1 (MD5) / Esta dissertação apresenta um estudo da aplicação da Transformada de Walsh-Hadamard (WHT) em diferentes sistemas OFDM. Os sistemas avaliados envolvem a transmissão sem fio entre uma antena transmissora e uma receptora (sistema SISO), e duas antenas transmissoras e uma receptora (sistema MISO Alamouti). A WHT espalha o sinal de informação antes de ser modulado no sistema OFDM. Conseqüentemente, os efeitos de desvanecimento provocados pelos canais correspondentes a cada subportadora OFDM também são espalhados, resultando em uma condição de desvanecimento médio destes canais. Isto leva a um aumento da robustez dos canais das subportadoras que mais sofreram com a transmissão puramente OFDM, mas degrada a condição de desvanecimento das mais robustas. Para verificar esta característica da WHT e o ganho de desempenho que ela possa impactar ao sistema OFDM, foram realizadas simulações com sistemas OFDM com e sem o uso da WHT. Assim, foi possível avaliar o desempenho desta técnica nos

<p> This thesis describes a proposed design of a special-purpose digital instrument that will obtain the first 32 coefficients of the Walsh-Fourier series of a low-fundamental frequency periodic voltage. The mathematics are developed for applying Walsh functions to obtain a Walsh-Fourier series in the same manner as sinusoidal waves are used to obtain a Fourier series of a periodic wave. It is shown how Walsh-Fourier coefficients are employed to obtain a Fourier series. Some familiar waveforms are shown as examples. The mathematical concepts are applied to the design of the instrument, of which two major portions have been constructed using integrated circuits. The Walsh-Fourier coefficients are available at the end of the second cycle of the input. The upper fundamental frequency limit of the instrument is approximately 60 Hz. There is no low-frequency limit.</p> / Thesis / Master of Engineering (MEngr)

<p> Walsh functions are defined both by recursive and non-r~cursive equations. A synopsis is given of the properties of Walsh functions relevant to this thesis. Two algorithms for simple evaluation of an arbitrary point on a Walsh function that use only the binary codes for the parameters of the Walsh function result from the non-r~cursive definitions. Direct hardware implementation of the evaluation algorithms yields programmable digital Halsh function generators. One of the generators, which produces functions that are free of hazards or ambigious states, is modified to produce a parallel array of Walsh functions. This generator is used in a Walsh Spectral Analyzer that evaluates simultaneously several Walsh series coefficients of an input signal. </p> <p> Walsh series analysis and the concepts of the design of a digital Walsh Spectral Analyzer are discussed. The equation that is used to determine a Walsh series coefficient is modified so that each portion of the equation can be manipulated conveniently by a digital instrument. Although the instrument was designed primarily to analyze periodic waves, extensions to the design can be made to accommodate aperiodic signals. Signals with frequencies from the audio range downwards can be analyzed by the Walsh Spectral Analyzer. </p> <p> Walsh series to Fourier series conversion is dealt with. It has been found that the Fourier coefficients of signals that are limited either in frequency or in sequency can be evaluated precisely using a finite number of Walsh coefficients of the same signal. A dual relationship holds for Fourier to Walsh series conversion. The Fourier series coefficients of Walsh functions comprise part of the conversion relationships. The Fourier transforms of Walsh functions, from which the above coefficients can be obtained, are derived in non-recursive form. </p> / Thesis / Doctor of Philosophy (PhD)