Controlling zeros of interpolating series

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Title: Controlling zeros of interpolating series
Author: Robinson, Jeffrey N.
Abstract: Some interesting problems arise when classical complex analysis techniques are applied to digital filter theory . Polynomials used in the interpolation of digital signals are called interpolating polynomials . These pol5momials may require modification to assure the convergence of their reciprocals on the unit circle . Such modifications were a principal concern of an earlier paper by R . Barnard , W . Ford and Y . Wang [4] . The distribution of zeros and the orthogonality property of {sinc (m >2 : )} enables the construction of an infinite interpolating series for digital signals to which classical results can be applied [4] . For practical purposes it is convenient to consider finite truncations of the infinite series PN - A property that was observed in [4] was that the polynomials obtained by truncating the interpolating series P^ had the property that all of their zeros lie on the unit circle . Natural generalizations of the sine functions are the Bessel functions , Gegenbauer and Jacobi polynomials , and polynomials generated by certain measures . In this paper , we consider polynomials which are obtained by truncating infinite series which are generalizations of the interpolating series P^ . We show that these polynomials do not have the property that their zeros lie on the unit circle when the infinite series is based on one of the above natural generalizations of the sine functions .
URI: http : / /hdl .handle .net /2346 /15304
Date: 2001-05

Citation

Controlling zeros of interpolating series. Master's thesis, Texas Tech University. Available electronically from http : / /hdl .handle .net /2346 /15304 .

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