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The Development of New Filter Functions Based Upon Solutions to Special Cases of the Sturm-Liouville Equation

Two common classes of filter functions in use today, Butterworth functions and Chebyshev functions, are based upon solutions to special cases of the Sturm-Liouville equation. Here, solutions to several other special cases of the Sturm-Liouville equation were used to develop filter functions, and the properties of the resulting filters were examined. The following functions were explored: Chebyshev functions of the second kind, untraspherical functions of the second and third kinds, Hermite functions, and Legendre functions. Filter functions were developed for each of the first five polynomials in each series of functions, and magnitude and phase responses were tabulated and plotted. One of the classes of functions, the Hermite functions, led to filters which have a significant advantage over the commonly used Chebyshev filters in passband magnitude response, and were essentially the same as Chebyshev filters in stopband magnitude response and phase response.

Identiferoai:union.ndltd.org:ucf.edu/oai:stars.library.ucf.edu:rtd-1402
Date01 October 1979
CreatorsChapman, Stephen Joseph
PublisherUniversity of Central Florida
Source SetsUniversity of Central Florida
LanguageEnglish
Detected LanguageEnglish
Typetext
Formatapplication/pdf
SourceRetrospective Theses and Dissertations
RightsPublic Domain

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