## 1 Introduction  
Brain-computer interface (BCI) systems were established for direct communication between the human brain and the external environment [1; 2; 3; 4; 5]. These systems act as communication channels for exchanging information and controlling external devices [5]. BCI systems, such as EEG, can measure signals of imagined movement modulation from the brain's electrical activity [6]. The origin of motor neuron activation is real movement or imagined movement. These two types of movement are somewhat similar in motor neuronal activation [7]. Different measurable EEG patterns were discovered based on different types of motor imagery. Different EEG signals, such as mu and beta rhythms, exhibit cortical potentials [8], event-related P300 [9; 10], and visual evoked potentials [11]. Motor imagery (MI) is one of the many types of BCI systems used in most studies over the past few decades. A motor imagery BCI (MI-BCI) is suitable and safe for noninvasive measurements. The advantages of motor imagery include an advanced approach to signal processing and minimal auxiliary equipment. The preprocessing, feature extraction, and pattern classification of EEG signals are core components of BCI systems. EEG signals consist of source brain signals and noise [12]. To simplify this problem, raw EEG signals can be considered linear. An essential part of BCI systems is the preprocessing step, which removes the noise. The next part is feature extraction, which is crucial. One well-known feature extraction approach for an MI-BCI is the common spatial pattern (CSP) [4; 13; 14]. CSP includes an effective feature extraction approach and a popular spatial filtering algorithm for two MI task classifications. For accurate classification, the effective parameters are the best frequency band and the associated filter parameters. The optimal frequency band highly depends on the user and the measurement. Hence, it is necessary to determine the optimal frequency band for each user or dataset separately. Many methods for solving the problem of finding effective parameters, such as the best frequency band and the associated filter parameters, have been proposed [15; 16; 17; 18]. To use CSP for the combination of two different signals (observed with time-delayed signals), the following methods have been introduced: (1) common spatial-spectral pattern (CSSP) [15] and (2) common sparse spectral-spatial pattern (CSSSP) [16]. These approaches obtain the coefficients of a finite impulse response (FIR) filter. CSSP has time-delay drawbacks and limitations. Hence, CSSP provides very poor frequency selectivity. Even with the time-delay limitation, CSSP can provide different spectral patterns for any channel. In comparison, CSSSP can provide different spectral patterns for all channels. The computational optimization of CSSSP is expensive. It requires high-cost and extensive parameter-tuning optimization of filter parameters. In the methods of the spectrally weighted common spatial pattern (SPEC-CSP) [17] and iterative spatial-spectral pattern learning (ISSPL) [18] for optimizing filters and spatial weights, iterative procedures are used. Therefore, for the spectrum, spatial weights and filter parameters are optimized by CSP and weights, which can be found using some criteria. This approach could solve the two optimization problems, i.e., finding the best frequency band and finding the associated filter parameters. Based on different cost functions, it is not guaranteed that these two problems will converge. The authors of [19] introduced the sub-band of the common spatial pattern (SBCSP) and the filter-bank common spatial pattern (FBCSP) [20] for sub-band decomposition. The main idea of these approaches is to decompose raw EEG signals into several frequency bands containing different pass bands as filter banks. CSP extracts the most discriminative features from each filter band, which increases the classification accuracy.