## 1 Introduction  
The electroencephalography (EEG) is a noninvasive brain examination, in which brain waves are measured on a skin surface of the subject's head. EEG is most often used by neurologists to differentiate functional from organic brain diseases, to diagnose sleep disorders, headaches, dizziness, to monitor brain activity during heart operations. EEG offers high temporal resolution which is not possible with magnetic resonance imaging (MRI). Since the EEG's history goes back to 1924 [1], the EEG signal analysis field is profoundly studied [2; 3; 4]. On the other side, there is whole field devoted to EEG signal modeling, which can be divided into three main categories [5]. Firstly, there are microscopic (detailed) models, focused on modeling individual neurons and their connections. Secondly, mesoscopic (reduced) models, in which neurons are modeled in less complex manner. Finally, macroscopic models, which simulate whole neuron networks without simulating individual neurons. In this paper, the third category is considered. First macroscopic model, considering only excitatory neural interactions, was introduced in 1956 by [PERSON] [6]. In 1972, [PERSON] and [PERSON] proposed a model with additional inhibitory interactions [7]. [PERSON], in 1975, proposed a spatial-temporal model [8], in opposition to only time-variant predecessors. Despite the simplicity of those models, they constitute the foundation of all the later ones [5], like [PERSON]'s [9], [PERSON]'s [10], or [PERSON]'s [11]. In this paper, the one-column Jansen-Rit (J-R) model was analyzed. The mathematical single-column model was developed by many researchers including [PERSON], [PERSON], and [PERSON] [10]. It is widely present in literature [10; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22]. In [10], the authors deeply analyzed the model, taking into account not only alpha waves, but also epileptic activity and bifurcations, with the emphasis put on the influence of the \(p\) parameter (so the representation of the activity exterior to the column). In [12], the authors focused on comparison between the one column J-R model, double column J-R model, and [PERSON]'s model. However, parameters of the models were adjusted to represent specific brain activities, without comparison to real signals. Authors of [14] extended the model and analyzed both real and simulated signals, with the focus on transition from sine to spike activities. Nonetheless, fitting the model to real signal was absent. In [16; 17], the J-R model was extended, however without explicit, numerical comparison to real signals. The one-column J-R model has been also used under stochastic and periodic driving, to study ictogenesis (progression from the interictal state to the seizure) [19]. In [20], the authors studied the dynamical interactions of cortical areas. In [21], the authors used Jansen-Rit model to develop an in silico platform to examine the effects of neighboring regions electrical stimulation on a another brain region. The authors of [22] analyzed the dynamics of a revised Jansen-Rit model in the stop-signal task. In 2012, the authors of [23] presented a method for estimating parameters in the J-R model using state observer. In the next year the method was implemented to estimate parameters of both modeled and real signals (which were obtained via subdural grid electrode) [24]. In 2016, the authors of [25] applied unscented Kalman filter to estimate the J-R model parameters in real time, while monitoring propofol-based anesthetic state (via EEG). Obtained parameters were used to classify anesthetic brain state. In the mentioned works, the parameters were being obtained in a continuous way; i.e., they constituted a parameter-time matrix, with a set of parameter values for each specific moment. This paper presents a different approach to obtaining J-R model parameters, which is an off-line method. Obtained parameters, like in previous works, could be used for signal classification. The parameters themselves, however, are obtained once for full duration of a signal.