Time-frequency analysis of heart murmurs. Part II: Optimisation of time-frequency representations and performance evaluation

The basic parameters of the spectrogram, the Choi-Williams, and the Bessel distributions are adjusted to provide the best time-frequency representations (TFRs) of the simulated murmur signals of mitral stenosis, mitral regurgitation, aortic stenosis, aortic regurgitation, and of two musical murmurs. The initial adjustment of the parameters of each TFR technique is performed by computing and minimising the relative averaged absolute error between the frequency contours at -3 dB and -10 dB of each TFR of the simulated murmurs and those of the theoretical distribution of the same signals. The results show that the spectrogram generally provides very good to excellent performance in representing the TFRs of stenotic and regurgitant murmurs. Improvements provided by the Choi-Williams and the Bessel distributions are minor but not systematic for the two signal-to-noise ratios tested (0 and 30 dB) and for the two frequency contours estimated. The Bessel and the Choi-Williams distributions provide the best performance for the musical murmurs. The study shows that although a single technique cannot be optimal for all six murmurs, the spectrogram using a Hamming window of 30 ms is an acceptable compromise to detect the six simulated heart murmurs.