Keywords

Electric filters, Sturm Liouville equation, Hermite-function filters, Chebyshev functions (second kind), Ultraspherical functions (second and third kinds), Legendre-function filters, Magnitude and phase response analysis

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

PDF

Pages

108 pages

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; Sturm-Liouville equation--Numerical solutions; Electric filters--Design; Electric filters--Mathematical models; Continuous-time filters--Design and construction; Eigenfunctions

Collection (Linked data)

Retrospective Theses and Dissertations

Accessibility Status

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Engineering Commons

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