Estimating Derivatives from Noisy Data: A Wavelet Multiresolution Decomposition Approach

Wavelet decompositions provide an excellent tool for localised approximation of functions with any degree of regularity at different scales and with a desired accuracy. This representation allows operations like differentiation and integration to be replaced by simple algebraic operations performed over the wavelet coefficients. In this context the task of differentiating discrete noisy data can be performed more efficiently. The present study analyses from both a theoretical and practical point of view, the problem of smoothing and differentiating experimental noisy signals within the framework of multiresolution decomposition, The algorithm proposed is tested on a numerical simulated example.