Reconstruction of Finite Signal Derivatives From Multiscale Extrema Representations: Application to Transient Estimation and Signal Approximation

In this correspondence, we propose a novel approach to the reconstruction of finite signal derivatives from the extrema of a multiscale representation, first introduced by Berkner. We show that this reconstruction procedure naturally leads to the definition of a signal characteristic scale. We also focus on signal approximation from the multiscale extrema representation of one of its derivatives. Numerical applications involve the use of the signal characteristic scale for transient estimation and also the study of the new signal approximation method we propose