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Type of Document	Dissertation
Author	Titsworth, Robert C.
URN	etd-09092005-130635
Persistent URL	http://resolver.caltech.edu/CaltechETD:etd-09092005-130635
Title	Correlation properties of cyclic sequences
Degree	PhD
Option	Electrical Engineering
Advisory Committee	Advisor Name Title Solomon W. Golomb Committee Chair
Keywords	none
Date of Defense	1962-01-01
Availability	unrestricted
Abstract In the unconstrained channel with additive Gaussian noise, where the optimum detector is based on correlation or matched filters, the quality of a code can be expressed as a function of the correlation values between code words. For a cyclic-sequence code, optimality reduces to a criterion to be met by the autocorrelation function of the sequence. Methods are presented here for determining cyclic sequences with given correlation properties. When the amount of equipment in the receiver is limited, matched filtering is no longer the optimal detection scheme. A better system, as is shown here, is one which, by the use of a Boolean function, combines several "component" sequences to generate the transmitted signal; the receiver consists of filters matched to each component. The logic, the number of components, the requirements of the component sequences to optimize the system, and a general method for treating Boolean logics are given in this work.
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