Walsh Functions Obtained from the Frame Multiplication of the Split-Extension of Hypercomplex Numbers

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dc.contributor.advisorLydia N. Njugunaen_US
dc.contributor.authorWachira, John Wang’ondu
dc.date.accessioned2021-11-05T09:13:19Z
dc.date.available2021-11-05T09:13:19Z
dc.date.issued2021
dc.descriptionA Project Submitted in Partial Fulfillment of the Requirement for the Award of the Degree of Master of Science in Pure Mathematics in the School of Pure and Applied Sciences of Kenyatta University, April 2021.en_US
dc.description.abstractCommunication theory was founded on the system of sine-cosine functions in 1927. However, the theory of Walsh functions is slowly replacing the theory of sine-cosine functions. Walsh functions use sequency while sine-cosine functions use frequency. The concept of frequency is a consequence of these functions, since frequency is defined as a parameter f in sin 2ᴨft and cos 2ᴨft. So far, Walsh functions are the only known functions with desirable features comparable to sine-cosine functions for use in communication. Walsh functions were first introduced in Mathematics by Joseph L. Walsh in 1923. Since then, various researchers have constructed Walsh functions using various techniques. In this project we constructed Walsh functions from the frame multiplication of the split-extension of hyper complex numbers. The multiplication tables for the basis elements of complex split extension, quaternion split extension and octonion split extension were considered.We then obtained matrices using the signs of the values from each of the tables.The rows in each of the matrices obtained were investigated to determine its properties.It is from these rows of each matrix that we constructed Walsh functions and determined the distinct number of the functionsen_US
dc.description.sponsorshipKenyatta Universityen_US
dc.identifier.urihttp://ir-library.ku.ac.ke/handle/123456789/22939
dc.language.isoenen_US
dc.publisherKenyatta Universityen_US
dc.subjectWalsh Functionsen_US
dc.subjectFrame Multiplicationen_US
dc.subjectSplit-Extensionen_US
dc.subjectHypercomplex Numbersen_US
dc.titleWalsh Functions Obtained from the Frame Multiplication of the Split-Extension of Hypercomplex Numbersen_US
dc.typeThesisen_US
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