Study of quadrature FIR filters for extraction of low-frequency instantaneous information in biophysical signals

Quadrature bandpass filters take a real-valued signal and output an analytic signal from which the instantaneous amplitude and phase can be computed. For this reason, they represent a useful tool to extract time-varying, narrow-band information from electrophysiological signals such as electroencephalogram (EEG) or electrocardiogram. One of the defining characteristics of quadrature filters is its null response to negative frequencies. However, when the frequency band of interest is close to 0 Hz, a careless filter design could let through negative frequencies, producing distortions in the amplitude and phase of the output. In this work, three types of quadrature filters (Ideal, Gabor and Sinusoidal) have been evaluated using both artificial and real EEG signals. For the artificial signals, the performance of each filter was measured in terms of the distortion in amplitude and phase, and sensitivity to noise and bandwidth selection. For the real EEG signals, a qualitative evaluation of the dynamics of the synchronization between two EEG channels was performed. The results suggest that, while all filters under study behave similarly under noise, they differ in terms of their sensitivity to bandwidth choice. In this study, the Sinusoidal filter showed clear advantages for the estimation of low-frequency EEG synchronization.