Interpolation by fast Fourier and Chebyshev transforms
Donald M. Monro · International Journal for Numerical Methods in Engineering · 1979
Abstract Transform methods for the interpolation of regularly spaced data are described, based on fast evaluation using discrete Fourier transforms. For periodic data adequately sampled, the fast Fourier transform (FFT) is used directly. With undersampled or aperiodic data, a Chebyshev interpolating polynomial is evaluated by means of the FFT to provide minimum deviation and distributed ripple. The merits of two kinds of Chebyshev series are compared. All the methods described produce an interpolation passing directly through the given values and are applied easily to the multi‐dimensional case.