Time-frequency analysis of the first heart sound. Part 2: An appropriate time-frequency representation technique

A simulated first heart sound (S1) signal is used to determine the best technique for analysing physiological S1 from the following five time-frequency representations (TFR): the spectrogram, time-varying autoregressive modelling, binomial reduced interference distribution, Bessel distribution and cone-kernel distribution (CKD). To provide information on the time and frequency resolutions of each TFR technique, the instantaneous frequency and the -3 dB bandwidth as functions of time were computed for each simulated component of the S1. The performance index for selecting the best technique was based on the relative error and the correlation coefficient of the instantaneous frequency function between the theoretical distribution and the computed TFR. This index served to select the best technique. The sensitivity of each technique to noise and to small variations of the signal parameters was also evaluated. The results of the comparative study show that, although important limitations were found for all five TFRs tested, the CKD appears to be the best technique for the time-frequency analysis of multicomponent signals such as the simulated S1.