Gaussian wavelet features and their applications for analysis of discretized signals (Q1973533)

Symmetric bell-shaped signals registered in a discrete form are considered. The problem is to evaluate location, amplitude and scale parameters from the perturbed discrete information in the presence of noise, detector uncertainties and the influence of other close signals. The authors present fast methods for reconstructing these signal parameters. The methods are based on the wavelet transform generated by Gaussian distribution functions \(g_n(x)=(-1)^{n+1}{{d^n}\over{dx^n}}e^{-x^2/2}\) for \(n=1,2,3,4.\) The results of numerical experiments indicate certain rule for optimal choosing of shift and dilation parameters. Monte Carlo simulations are applied to show a high accuracy and efficiency of the proposed methods.