Adaptive function approximation based on the Discrete Cosine Transform
  (DCT)
Ana I. Pérez-Neira Marc Martinez-Gost Miguel Ángel Lagunas
This paper studies the cosine as basis function for the approximation of
univariate and continuous functions without memory. This work studies a
supervised learning to obtain the approximation coefficients, instead of using
the Discrete Cosine Transform (DCT). Due to the finite dynamics and
orthogonality of the cosine basis functions, simple gradient algorithms, such
as the Normalized Least Mean Squares (NLMS), can benefit from it and present a
controlled and predictable convergence time and error misadjustment. Due to its
simplicity, the proposed technique ranks as the best in terms of learning
quality versus complexity, and it is presented as an attractive technique to be
used in more complex supervised learning systems. Simulations illustrate the
performance of the approach. This paper celebrates the 50th anniversary of the
publication of the DCT by Nasir Ahmed in 1973.