A New Method for Chebyshev Polynomial Interpolation Based on Cosine Transforms

Bing Zhao Li; Yan Li Zhang; Xian Wang; Qi Yuan Cheng

doi:10.1007/s00034-015-0087-4

A New Method for Chebyshev Polynomial Interpolation Based on Cosine Transforms

Bing Zhao Li^*, Yan Li Zhang, Xian Wang, Qi Yuan Cheng

^*Corresponding author for this work

School of Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	719-729
Number of pages	11
Journal	Circuits, Systems, and Signal Processing
Volume	35
Issue number	2
DOIs	https://doi.org/10.1007/s00034-015-0087-4
Publication status	Published - 1 Feb 2016

Keywords

Chebyshev nonuniform sampling
Chebyshev polynomial
Coefficients
Discrete cosine transform
Error analysis
Polynomial interpolation

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10.1007/s00034-015-0087-4

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title = "A New Method for Chebyshev Polynomial Interpolation Based on Cosine Transforms",

abstract = "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.",

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T1 - A New Method for Chebyshev Polynomial Interpolation Based on Cosine Transforms

AU - Li, Bing Zhao

AU - Zhang, Yan Li

AU - Wang, Xian

AU - Cheng, Qi Yuan

PY - 2016/2/1

Y1 - 2016/2/1

N2 - 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.

AB - 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.

KW - Chebyshev nonuniform sampling

KW - Chebyshev polynomial

KW - Coefficients

KW - Discrete cosine transform

KW - Error analysis

KW - Polynomial interpolation

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JO - Circuits, Systems, and Signal Processing

JF - Circuits, Systems, and Signal Processing

IS - 2

ER -

A New Method for Chebyshev Polynomial Interpolation Based on Cosine Transforms

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