A New Method for Chebyshev Polynomial Interpolation Based on Cosine Transforms

Interpolation plays an important role in the areas of signal processing and applied mathematics. Among the various interpolation methods, those related to Chebyshev polynomial interpolation have received much interest recently. In this paper, we propose a new interpolation method using a type I discrete cosine transform (type I DCT) and the nonuniform roots of the second type of Chebyshev polynomials. In this method, the interpolation coefficients are derived using the type I DCT of the Chebyshev nonuniform sampling points. Simulations show the correctness of the proposed method, and a comparison of the proposed method with existing methods is also discussed in detail.