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

Prony´s method is found to be a very effective method for the analysis-synthesis of transient data. However, straightforward application of this method can lead to poor performance, especially for short and noisy data records. The authors present a new over-determined 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 cross-correlation 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 cross-correlation 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 upto 10%, and upto 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