Graduate Thesis Or Dissertation
 

On extension of the generalized sampling theorem

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  • The relation of the sampling theorem, developed by Shannon for Information Theory, to the Whittaker interpolatory functions is investigated and further extensions in this direction are suggested. The theory of the Shannon sampling theorem with its application in Information Theory is reviewed. The Kramer generalization of this theorem is illustrated for many more functions of interest in Mathematical Physics, so the use of this theorem in other fields besides communications is suggested. Campbell's question concerning the possibility of reducing Kramer's sampling theorem to that of Whittaker is investigated and illustrated for more functions of interest. Some useful theorems in this direction are proposed and proved. It is shown that although most illustrative functions satisfy Campbell's conditions, the advantage of Kramer's sampling theorem over that of Whittaker is removed only in the mind of the communications engineer, who is mainly interested in no integral transforms other than the celebrated Fourier Transform.
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file details JerriAbdulJabbarHassoon1967.pdf 2017-08-01 Público Baixar