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UBC Theses and Dissertations

Transfer functions with flat magnitude and flat delay Riml, Otfried Carl


The-coefficient and pole-zero locations of a transfer function F(s) having m zeros and n poles may be determined by imposing a total of (m+n-l) conditions on the magnitude and phase of F(s) at the origin. If q of these conditions are used to adjust the first q even derivatives of the magnitude of F(s), then (m+n-l-q) conditions may be used to adjust the first (m+n-l-q) even derivatives of the phase slope. By varying these indices m, n, and q, a family of functions may be obtained in which the Butterworth and Bessel-polynomial functions are special cases. A new approach described in this thesis yields some transfer functions which have not been treated in the literature. The step-function response is studied for the realizable solutions, and the relative merits of emphasizing flat magnitude and flat delay are compared.

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