Gilbert Walter - February Fourier Talks 2014
Professor Gilbert Walter (University of Wisconsin, Milwaukee) delivers his talk for the February Fourier Talks 2014 on February 20, 2014 at the University of Maryland, College Park.
www.fft2014.org
Title: Series of Chromatic Differences
Abstract: Chromatic series constitute an alternative to Taylor series which work better for band-limited functions. Their coefficients are based on derivative operators constructed from orthogonal polynomials on a finite real interval. However their use in applications shares a shortcoming with Taylor series in that they both require an input involving derivatives. We discuss a variation based on orthogonal polynomials on a circle instead of an interval. This leads to finite differences instead of derivatives for calculating the coefficients and results in generalizations of the Shannon Sampling Theorem.