A New Method for Chebyshev Polynomial Interpolation Based on Cosine Transforms

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• 作者：Bing-Zhao Li ; Yan-Li Zhang ; Xian Wang…
• 关键词：Chebyshev polynomial ; Chebyshev nonuniform sampling ; Polynomial interpolation ; Coefficients ; Discrete cosine transform ; Error analysis
• 刊名：Circuits, Systems, and Signal Processing
• 出版年：2016
• 出版时间：February 2016
• 年：2016
• 卷：35
• 期：2
• 页码：719-729
• 全文大小：675 KB
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• 作者单位：Bing-Zhao Li (1) (2)
  Yan-Li Zhang (1) (2)
  Xian Wang (1) (2)
  Qi-Yuan Cheng (1)
  
  1. School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, China
  2. Beijing Key Laboratory of Fractional Signals and Systems, Beijing, China
  
• 刊物类别：Engineering
• 刊物主题：Electronic and Computer Engineering
  
• 出版者：Birkh盲user Boston
• ISSN：1531-5878

文摘

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.