A Note on Least Squares Fitting of Signal Waveforms

Abstract

Some signal waveforms are very fast dampening oscillatory time series composed of exponential functions. The regular least squares fitting techniques are often unstable when used to fit exponential functions to such signal waveforms since such functions are highly correlated. Of late, some attempts have been made to estimate the parameters of such functions by Monte Carlo based search/random walk algorithms. In this study we use the Differential Evaluation based method of least squares to fit the exponential functions and obtain much more accurate results.

Keywords: Signal waveform, exponential functions, Differential Evolution, Global optimization, Nonlinear Least Squares, Monte Carlo, Curve fitting, parameter estimation, Random Walk, Search methods, Fortran

JEL Classification: C13, C15, C16, C63