Polynomial approximation of signals corrupted by noise

The polynomial approximation is a very useful procedure for the optimization of the design of electronic equipment. This procedure is more complex when the function to be processed is perturbed by noise. Exploiting the connection between wavelets and polynomials and the well known abilities of the Discrete Wavelet Transform to denoise, in this paper is proposed a new method for the accurate polynomial approximation of a function, despite the noise that perturbs it. This method can be used to enhance the estimation of any polynomial function perturbed by noise. Examples, containing applications of the proposed method, are also presented. The good simulation results obtained recommend the use of the proposed method in any difficult estimation problem.