The Chebyshev polynomial fitting properties of discrete cosine transform

摘要

In this paper, the least-squares approximation/fitting aspects of discrete cosine transform (DCT) are identified and analyzed. Through constructing a monovariant function skillfully defined on a discrete set, we obtain a specified series expansion which is a combination of Chebyshev polynomials. It will be shown that the corresponding Chebyshev polynomial expansion is exactly a mathematical equivalence of DCT.