Keywords
Electric filters, Sturm Liouville equation
Abstract
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.
Notes
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Graduation Date
Fall 1979
Advisor
Harden, Richard C.
Degree
Master of Science (M.S.)
College
College of Engineering
Degree Program
Engineering
Format
Pages
108 p.
Language
English
Rights
Public Domain
Length of Campus-only Access
None
Access Status
Masters Thesis (Open Access)
Identifier
DP0013262
Subjects
Electric filters, Sturm Liouville equation
STARS Citation
Chapman, Stephen Joseph, "The Development of New Filter Functions Based Upon Solutions to Special Cases of the Sturm-Liouville Equation" (1979). Retrospective Theses and Dissertations. 403.
https://stars.library.ucf.edu/rtd/403
Contributor (Linked data)
University of Central Florida. College of Engineering [VIAF]
Collection (Linked data)
Accessibility Status
Searchable text