Algorithms to estimate the instantaneous-frequency of a respiratory time-varying sequence

Resumen

On various occasions, algorithms to estimate instantaneous-frequency from a cyclic (seasonal) sequence to detect slow changes are needed. That is the case of the estimation of the variations of the respiratory rate for diagnostic purposes. There are a few possible procedures to estimate such an instantaneous-frequency, but without a thorough assessment to compute the respiration rate from a volumetric surrogate signal. This paper discusses the implementation of some algorithms for instantaneous-frequency estimation in MATLAB, comparing their performance from known synthetic signals, which resemble real-world respiratory signals, by using the goodness of fit parameters. We used a method based on the first conditional spectral moment of the time-frequency distribution of the input signal x, and other using the derivative of the phase of the analytic signal of x (found using the Hilbert transform). We also used methods based on second-order auto-regressive models. We computed the goodness of fit (maximum absolute and mean-squared errors) between the estimated and the expected ideal instantaneous-frequencies. The root MUSIC algorithm outperforms the others under assessment, showing its superiority for instantaneous-respiratory frequency estimation from a volumetric surrogate signal.