<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)
| Identifer | oai:union.ndltd.org:mcmaster.ca/oai:macsphere.mcmaster.ca:11375/20185 |
| Date | 06 1900 |
| Creators | Siemens, Karl-Hans |
| Contributors | Kitai, R., Electrical Engineering |
| Source Sets | McMaster University |
| Language | English |
| Detected Language | English |
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