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 representat ion of transient nonlinear chirp signals for modeling the aortic (A2) and t he pulmonary (P2) components of the second heart sound (S2), It is demonstr ated that each component is a narrow-band signal with decreasing instantane ous 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 orde r of thirty. A dechirping approach is used to obtain the instantaneous ampl itude of each component while reducing the effect of the background noise. The analysis-synthesis procedure is applied to 32 isolated A2 and 32 isolat ed P2 components recorded in four pigs with pulmonary hypertension. The mea n +/- standard deviation of the normalized root-mean-squared error (NRMSE) and the correlation coefficient (rho) between the original and the synthesi zed signal components were: NRMSE = 2.1 +/- 0.3% and rho = 0.97 +/- 0.02 fo r A2 and NRMSE = 2.52 +/- 0.5% and rho = 0.96 +/- 0.02 for P2. These result s confirm that each component can be modeled as mono-component nonlinear ch irp signals of short duration with energy distributions concentrated along its decreasing instantaneous frequency.