Fast computation of Chebyshev optimal nonuniform interpolation

Abstract

There are two schemes of Chebyshev interpolation. Neagoe (1990) recently developed an approach, using the existing DCT algorithms, for computing the Chebyshev coefficients for one of the two schemes, but no algorithms have been developed for computing the interpolated samples. In this paper we first demonstrate that both schemes of Chebyshev interpolation relate to the type I and II discrete cosine transforms (DCT-I and DCT-II), respectively. Then we show that both schemes of Chebyshev interpolation can be computed using the existing fast algorithms for the DCT.