Nonlinear transient chirp signal modeling of the aortic and pulmonary components of the second heart sound

This paper describes a new approach based on the time-frequency representation of transient nonlinear chirp signals for modeling the aortic (A2) and the pulmonary (P2) components of the second heart sound (S2). It is demonstrated that each component is a narrow-band signal with decreasing instantaneous frequency defined by its instantaneous amplitude and its instantaneous phase. Each component is also a polynomial phase signal, the instantaneous phase of which can be accurately represented by a polynomial having an order of thirty. A dechirping approach is used to obtain the instantaneous amplitude of each component while reducing the effect of the background noise. The analysis-synthesis procedure is applied to 32 isolated A2 and 32 isolated P2 components recorded in four pigs with pulmonary hypertension. The mean +/- standard deviation of the normalized root-mean-squared error (NRMSE) and the correlation coefficient (rho) between the original and the synthesized signal components were: NRMSE = 2.1 +/- 0.3% and rho = 0.97 +/- 0.02 for A2 and NRMSE = 2.52 +/- 0.5% and rho = 0.96 +/- 0.02 for P2. These results confirm that each component can be modeled as mono-component nonlinear chirp signals of short duration with energy distributions concentrated along its decreasing instantaneous frequency.