摘要： 文章首先利用Chebyshev多项式插值与DCT(离散余弦变换)变换之间的相互关系,提出了基于第一类Chebyshev多项式的第N次多项式的零点作为非均匀取样点的DCT变换方法。然后根据Chebyshev展开式良好的下降特性,证明了文章提出的非均匀取样的DCT变换与传统的均匀取样DCT变换相比在信号的压缩倍数和压缩质量方面所具有的良好特性。并通过两个实例给予说明。此外文章还就取样点和取样频率的选取对结论的影响作了讨论。

关键词: 非均匀取样, Chebyshev多项式, 插值, 离散余弦变换

Abstract: In this paper, We firstly present a nonuniform sampling DCT method based on the relationship of Chebyshev polynomial interpolation and DCT, in which, the sampling points are chosen as zeros of Nth degree Chebyshev polynomials of the first kind. Then according to the good decreasing property of Chebyshev expantion, we prove the better characteristics of nonuniform sampling DCT in compression ratio and compression quality comparing with uniform sampling DCT. Two examples are given in this paper. Also some discussions about sampling frequency and the selection of sampling points are made.

中图分类号: 

• TN911.6