The goal of this work is to describe the underlying theoretical and algorithmic basis of a MATLAB-based software developed by the authors. The software is intended for investigation of time series (signals) which can be modeled as the sum of real-valued quasipolynomials plus white noise. With the help of the software described, one can compute the expressions of the Cramér-Rao lower bound on the covariance matrix of the estimation error of unbiased estimates of damping factors and frequencies of quasipolynomials and to obtain estimates of these parameters using three versions of Prony method. Using this software, one can generate various models of quasipolynomials, obtain plots of their poles with respect to the unit circle, compute and plot 2σ-bounds (where σ is given by the CRB formula) around each pole, and also pole estimates obtained in each realization. Results of numerical experiments are presented.