Modified forward-backward overdetermined Prony's method and its application in modelling heart sounds

Prony's method is found to be a very method for the analysis-synthesis of data, straightforward However, application of this method can lead to poor performance, especially for short and noisy data records, The authors present a new overdetermined forward-backward Prony method (MFBPM) and its application to the analysis of the first and second heart sounds. The accuracy of the method is measured using both crosscorrelation and the normalised-mean-square-error (NMRSE) between a real signal and a synthetic one. Results from more than 80 different subjects show that the MFBPM is highly stable and gives very good performance with an average crosscorrelation coefficient of 99.62%. Comparison of the results based on the NMRSE criterion show that the MFBPM is more precise than the modified backward Prony method (MBPM) with an accuracy improvement of up to 10% and up to 20% when compared with the conventional forward-backward Prony method (FBPM), Furthermore, a new method for dynamic estimation of model order is proposed for the case of heart sounds based on a subset of synthesised heart sounds which best approximates the observed data using NMRSE.