Dyadic aggregated autoregressive (DASAR) model for time-frequency representation of biomedical signals

This paper introduces a new time-frequency representation method for biomedical signals: the dyadic aggregated autoregressive (DASAR) model. Signals, such as electroencephalograms (EEGs) and functional near-infrared spectroscopy (fNIRS), exhibit physiological information through time-evolving spectrum components at specific frequency intervals: 0-50 Hz (EEG) or 0-150 mHz (fNIRS). Spectrotemporal features in signals are conventionally estimated using short-time Fourier transform (STFT) and wavelet transform (WT). However, both methods may not offer the most robust or compact representation despite their widespread use in biomedical contexts. The presented method, DASAR, improves precise frequency identification and tracking of interpretable frequency components with a parsimonious set of parameters. DASAR achieves these characteristics by assuming that the biomedical time-varying spectrum comprises several independent stochastic oscillators with (piecewise) time-varying frequencies. Local stationarity can be assumed within dyadic subdivisions of the recordings, while the stochastic oscillators can be modeled with an aggregation of second-order autoregressive models (ASAR). DASAR can provide a more accurate representation of the (highly contrasted) EEG and fNIRS frequency ranges by increasing the estimation accuracy in user-defined spectrum region of interest (SROI). A mental arithmetic experiment on a hybrid EEG-fNIRS was conducted to assess the efficiency of the method. Our proposed technique, STFT, and WT were applied on both biomedical signals to discover potential oscillators that improve the discrimination between the task condition and its baseline. The results show that DASAR provided the highest spectrum differentiation and it was the only method that could identify Mayer waves as narrow-band artifacts at 97.4-97.5 mHz.