Chebyshev nonuniform sampling cascaded with the discrete cosine transform for optimum interpolation

A method for discrete representation of signals consisting of a cascade of Chebyshev nonuniform sampling (CNS) followed by the discrete cosine transform (DCT) is presented. It is proven that the considered signal samples and the coefficients of the corresponding Chebyshev polynomial finite series are essentially a discrete cosine transform pair. A method for fast computation of the coefficients of the optimum interpolation formula (which minimizes the maximum instantaneous error) is provided. If the signal g(t) is band-limited and has a finite energy, the condition of convergence for interpolation can be deduced