## 1 Introduction  
Brain-machine interface (BMI) technology is aimed at acquiring and analyzing brainwave signals for device control [1, 2]. BMI technology is used in fields [3] such as medicine, healthcare [4], education, and entertainment [5]. For example, patients can drive their wheelchairs [6], operate prosthetic hands [7], and control computer keyboards using their brainwave signals. Therefore, BMI can be used to address mobility inconveniences and speech difficulties caused by disabilities.  
The quantity and quality of the data available for classification are important factors for the accurate estimation of a user's intention [8]. However, most BMI systems suffer from a lack of data because the acquisition of bio-signals requires stressful experiments. Various data augmentation techniques have been developed to address this issue, including noise addition methods, generative adversarial networks (GANs), and covariance matrix decomposition (CMD) methods. Noise addition methods generate artificial datasets by adding noise vectors to the original data [9, 10, 11, 12]. For example, [PERSON] et al. [11] added a Gaussian noise signal (with zero mean and unit variance) to electroencephalogram (EEG) signals to generate artificial EEG signals. However, this method adds simple noise without considering the stochastic characteristics of the bio-signal of interest. Therefore, a quality artificial dataset is not guaranteed when using this method.  
GANs automatically learn the properties of the target bio-signal by using competitive networks (i.e., generator and discriminator) [13, 14, 15, 16]. [PERSON] et al. [15] suggested a conditional Wasserstein GAN for EEG data augmentation to improve the accuracy of emotion recognition. [PERSON] and [PERSON] [16] used a conditional deep convolutional GAN method to generate artificial EEG data. However, GANs require a long training time and a large number of data samples [17]. Therefore, when only a small number of bio-signal samples are available, a GAN cannot generate high-quality artificial data.  
CMD methods have been widely used to create stochastic signals because they consider the correlation between features [18; 19; 20; 21]. CMD does not require complicated training; thus, its calculation time is very short. Furthermore, CMD provides high-quality data without an extremely large database. Owing to these advantages, CMD is an adequate data augmentation technique for bio-signals. CMD-generated artificial datasets increase the classification accuracy for brainwave, electromyography, and electrocardiography signals [21; 22]. Therefore, in this study, CMD was used to generate artificial brainwave signals.  
Accordingly, this study aimed to develop a more flexible CMD model than previous CMD models. CMD requires random noise to synthesize the artificial data. To preserve the correlations observed in the original data, the mean of the random noise should be zero, and its variance must be uniform. However, previous models impose another restriction on this random noise; they use only a standard normal distribution, even though this restriction is not related to correlation preservation. Thus, this study focused on releasing this restriction to provide greater flexibility to the CMD. The proposed model modifies the skewness and kurtosis of random noise by using a generalized normal distribution (GND). Then, the effects of skewness and kurtosis on accuracy were investigated for brainwave signals.  
The remainder of this paper is organized as follows. Section 2 describes the motor imagery brainwave dataset used in this study and provides a detailed description of the proposed CMD method. Section 3 describes the artificial brainwave signals generated by the proposed method. The classification accuracies over different values of GND skewness and kurtosis are also compared. Finally, Section 4 summarizes the study and concludes this paper.