Adaptive function approximation based on the Discrete Cosine Transform (DCT)

TL;DR

This paper introduces a supervised learning approach for function approximation using the Discrete Cosine Transform (DCT), leveraging its orthogonality and finite dynamics to improve convergence and accuracy.

Contribution

It proposes a novel supervised learning method for DCT-based function approximation, enhancing convergence control and simplicity over traditional transform methods.

Findings

Supervised learning with DCT outperforms traditional methods in approximation quality.

Normalized Least Mean Squares (NLMS) benefits from DCT's properties for faster convergence.

The technique is computationally simple and effective for complex supervised learning systems.

Abstract

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.