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

Abstract

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.

Cluster analysis and classification of heart sounds

“…There is no consensus in the literature regarding the most suitable time-frequency representation of S1. Different studies point out different techniques such as the binomial transform [13], cone-kernel distribution [15] and continuous wavelet transform [14] as the best choices. Indeed, when considering the problem of accurate decomposition of the signal into its subcomponents, there are marked differences between methods.…”

“…Their concurrent variability in both time and frequency domains makes joint time-frequency analysis a favorable method of decomposition and representation. Time-frequency representations, including shorttime Fourier transform, Wigner-Ville distribution, continuous wavelet transform and reduced-interference distributions have been previously applied to heart sound signals [13][14][15]. These nonparametric methods have been shown useful in characterizing the sub-components of the first and second heart sounds and extracting meaningful spectral features from them, with good performance compared to parametric modeling techniques [16].…”

Haemodynamic determinants of the mitral valve closure sound: A finite element study

“…The presence of signal processing artifact has been discussed by many authors (see, for example) DURAND and PIBAROT (1995), CHEN and DURAND (1997a), WOOD and BARRY (1995), XU and DURAND (2000;, WOOD and BUOA, (1992), BARRY and WOOD (1991) and DURAND and Guo (1992)) and must motivate those in the field to seek better, higher-resolution time-frequency decompositions. We have deliberately avoided the question of whether the radial Gaussian kernel adopted in this paper is the most appropriate for decomposing S1 in timefrequency, instead, we have preferred to focus on the mechanics of the first heart sound generation, in doing so, we have created the first computational model to account for fluid-structure interaction in mitral mechanics and the first model, consequently, to predict the non-stationary character of the sound associated with mitral valve closure.…”

Assessment of time–frequency representation techniques for thoracic sounds analysis

“…Again, in the former equation l represents the discrete time index [33]. For this figure of merit, the TFR with the IF value closer to one is associated with the best performance.…”

“…where IF i (l) and IF e (l) correspond to the instantaneous frequencies obtained from the ideal and estimated TFR, respectively, and l represents the discrete time index [33]. Estimation of the instantaneous frequencies in (21) was done by means of the first moment of TFRs as in [34].…”