Discrete_Chebyshev_transform
In applied mathematics, a discrete Chebyshev transform (DCT) is an analog of the discrete Fourier transform for a function of a real interval, converting in either direction between function values at a set of Chebyshev nodes and coefficients of a function in Chebyshev polynomial basis. Like the Chebyshev polynomials, it is named after Pafnuty Chebyshev.
The two most common types of discrete Chebyshev transforms use the grid of Chebyshev zeros, the zeros of the Chebyshev polynomials of the first kind and the grid of Chebyshev extrema, the extrema of the Chebyshev polynomials of the first kind, which are also the zeros of the Chebyshev polynomials of the second kind . Both of these transforms result in coefficients of Chebyshev polynomials of the first kind.
Other discrete Chebyshev transforms involve related grids and coefficients of Chebyshev polynomials of the second, third, or fourth kinds.