A New Method for Chebyshev Polynomial Interpolation Based on Cosine Transforms
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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.
KeywordsChebyshev polynomial Chebyshev nonuniform sampling Polynomial interpolation Coefficients Discrete cosine transform Error analysis
The authors would like to thank the academic editor and anonymous reviewers for their valuable comments and suggestions. The authors would also like to thank Prof. Huafei Sun and Dr. Didar of the Beijing Institute of Technology for many discussions about and proofreading of the manuscript.
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