Synthesis of HRV signals characterized by predetermined time-frequency structure by means of time-varying ARMA models

In this paper we present two methodologies to generate heart rate variability (HRV) signals characterized by controlled and real-like time-frequency (TF) structure to be used to assess different methods of non-stationary HRV analysis. The synthesized signals are stochastic processes whose TF structure is predetermined by choosing either the time-course of the instantaneous frequencies and powers or the shape of the TF model function. They consist of three steps: (a) choice of the desired TF structure of the signals by choosing a set of design parameters; (b) automatic identification of the parameters of the corresponding models via simple closed-form expressions; (c) synthesis of the desired stochastic signals. Two measures to evaluate the goodness of the simulated signals are also given. Using this framework we were able to model the wide range of non-stationarities observed in heart rate modulation during exercise stress testing and experiments of music-induced emotions. We used the proposed methodology to assess the capability of the smoothed pseudo Wigner–Ville distribution (SPWVD) to quantify HRV patterns. We observed that the SPWVD followed the temporal evolution of the spectral components even when sudden and sharp transitions occur.