## 1 Introduction  
To help patients with functional motor disabilities, such as amyotrophic lateral sclerosis (ALS) or spinal cord injury (SCI), Brain-Computer Interface (BCI) has been researched for over decades. BCI is a system that establishes an artificial communication pathway between the central nervous system and external devices, acting as a peripheral motor, when a biological neuron path is weak, or no longer works properly [1]. Various applications applying BCI to real-world problems have been carried out: brain-actuated speller where a patient could type words on a computer screen with their thought [2, 3]; controlling computer cursor by gazing [4]; controlling incoming calls [5]; computer control interface [6]. Owing to the emerging advances in novel signal processing and computational algorithms, BCI has an important role in facilitating the recovery of neural functions, restoring functional corticospinal, and corticomuscular connections and neurorehabilitation. The non-invasive electroencephalography (EEG) technique has been widely used in BCI research because of its clinical simplicity, cost efficiency, and safety [7]. Event-related desynchronization/synchronization (ERD/ERS), in which the amplitude of mu and beta rhyths is suppressed or increased depending on the event [8; 9; 10], is one of the main types of non-invasive BCI. Specifically, motor imagery (MI) elicits mu and beta ERD/ERS patterns in both healthy subjects as well as patients with severe motor disabilities [11; 12]. MI has the advantage over other methods as it only requires mental simulation of movements without actual actions or external stimuli. In recent years, many studies put their focus on investigating and reinforcing feature extraction and classification algorithms for MI-based BCI, thus enhancing BCI performance. Traditional feature extractors have been widely used and claimed to be effective up to now, however, they still have drawbacks. For example, the temporal resolution and spectral resolution of the short-time Fourier transform (STFT) algorithm are determined by the width of the time window [13]. That is to say, there is a trade-off between temporal and spectral resolution: the better the frequency resolution as the window gets wider, the worse the time resolution and vice versa. Another example is wavelet transform, which can perform multi-scale time-frequency analysis. The main disadvantage of this algorithm is that it requires manual screening for statistical features such as maximum, minimum, mean, and standard deviation of wavelet coefficients, whereas EEG pattern, motor imagery to be specific, is not stationary and it varies among subjects [14]. Meanwhile, common spatial pattern (CSP) is one of the promising candidates for the shortcoming of EEG low spatial resolution characteristic [15]. Moreover, the CSP algorithm, one of the most effective filters optimizing spatial information in motor tasks discrimination [16; 17], has not been fully investigated. Since CSP needs to identify discriminative frequency bands for effective classification, there is a substantial amount of studies on finding optimal frequency bands. The first approach is a combination of CSP and time-frequency analysis [18; 19]. The simultaneous optimization of the spatial spectrum filter is used in the second type [20; 21]. The third type of approach involves filtering the original EEG signals into multiple frequency sub-bands, then CSP is applied to extract features from these sub-bands, and classification is performed based on the optimum frequency bands [22; 23; 24; 25]. The intelligent optimization method is the fourth kind of technique utilized to determine the optimum frequency bands. This approach is capable of selecting informative frequency bands of any length and is independent of subjective experience [26; 27; 28]. In the first method, because frequency information is obtained via a time-frequency analysis, the EEG signals of each channel must be decomposed, which involves numerous calculations and takes considerable computation time.