ERD estimation algorithms

First, we used an FFT algorithm as the conventional method to probe the motor-imagery-related ERDs [8, 10, 12, 15, 19, 20]. According to these previous studies, EEG data were processed using the following 4 steps: (1) segmentation of 1-s time windows with 99% overlap; (2) power spectrum density calculation by FFT algorithm with a Hanning window; (3) determination of a frequency of interest (FOI), which showed the most significant ERD over the alpha bands by visual inspection in Screening session (see Experimental procedures in the Methods section); and (4) ERD transformation [15]. The algorithm of the motor-related ERD was defined as follows:

where A is the power spectrum density (PSD) of the EEG signal and R is the PSD of the baseline period from 3 to 5 s in each resting phase at time t and frequency f, which was most reactive frequency displaying ERD over the alpha band during the kinesthetic motor imagery task in the screening session.

Second, we used LIA-based algorithm as a novel estimation method [24]. According to the previously established algorithm with LIA [24], EEG data were processed using the following 4 steps: (1) determination of a FOI; (2) applying a narrow band-pass filter (FOI ± 1 Hz) using a second-order Butterworth band-pass filter with a 1-s time window; (3) LIA process (i.e. point-by-point multiplication and integration of the input signal with a reference trigonometric basis signal) with segmentation of 1/FOI s with a 99% overlap time window; and (4) ERD transformation [15].

In briefly, the previous study suggested that the averaged time delays by the online LIA algorithm (200 ± 9.49 ms) were around 300 ms shorter than those by the online FFT algorithm (503 ± 18 ms) [24]. In addition, the accuracy and stability to detect amplitude modulation of motor-imagery-related ERDs by the online LIA algorithm were significantly higher than those calculated by the online FFT algorithm (p < 1.0*10–10, p < 1.0*10–9, respectively) [24].