February Fourier Talks 2014

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.