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On computing Chebyshev optimal nonuniform interpolation
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DOI：10.1016/0165-1684(96)00045-X.png)
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Abstract
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In classical interpolation theory, there are two schemes of interpolation using Chebyshev polynomials, and two different signal sampling procedures. Neagoe recently developed an approach, using existing DCT algorithms, for computing the Chebyshev coefficients for one of the two schemes, but no algorithms have been developed for computing the interpolated samples. In this paper we first demonstrate that both schemes of interpolation using Chebyshev polynomials relate to the types I and II discrete cosine transform (DCT-I and DCT-II), respectively. Then we show that these schemes of interpolation using Chebyshev polynomials can be computed using existing fast algorithms for the DCT.
Keywords:
Chebyshev polynomial
interpolation
discrete cosine transform
fast algorithm
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