Over the last few decades, the Brain-Computer Interfaces have been gradually making their way to the epicenter of scientific interest. Many scientists from all around the world have contributed to the state of the art in this scientific domain by developing numerous tools and methods for brain signal acquisition and processing. Such a spectacular progress would not be achievable without accompanying technological development to equip the researchers with the proper devices providing what is absolutely necessary for any kind of discovery as the core of every analysis: the data reflecting the brain activity. The common effort has resulted in pushing the whole domain to the point where the communication between a human being and the external world through BCI interfaces is no longer science fiction but nowadays reality. In this work we present the most relevant aspects of the BCIs and all the milestones that have been made over nearly 50-year history of this research domain. We mention people who were pioneers in this area as well as we highlight all the technological and methodological advances that have transformed something available and understandable by a very few into something that has a potential to be a breathtaking change for so many. Aiming to fully understand how the human brain works is a very ambitious goal and it will surely take time to succeed. However, even that fraction of what has already been determined is sufficient e.g., to allow impaired people to regain control on their lives and significantly improve its quality. The more is discovered in this domain, the more benefit for all of us this can potentially bring.

This paper presents a new modification of the least-squares Prony's method for power-quality analysis in terms of estimation of harmonics and interharmonics in an electric power signal. The so-called reduced Prony's method can be competitive, in some specific case, to the Fourier transformation method and the classical LS Prony's method. The modification constitutes in a specific selection of a constant frequency vector in a Fourier-like manner leading to a remarkable reduction of the computational burden and enabling online real-time computations. In addition, a sampling frequency and an analysis window length can be selected to provide the numerical stability of the new algorithm.

Variable-Frequency Prony Method in the Analysis of Electrical Power Quality: The article presents a new modification of the the least squares Prony method. The so-called variable-frequency Prony method can be a useful tool for estimating parameters of sinusoidal components, which, in the analyzed signal, are characterized by time-dependent frequencies. The authors propose use of the presented method for testing the quality of electric energy. It allows observation of phenomena which, when using traditional methods, are averaged in the analysis window. The proposed modification of least squares Prony method is based on introduction and specific selection of a frequency matrix. This matrix represents frequencies of estimated components and their variability in time.

Off-the-shelf, consumer-grade EEG equipment is nowadays becoming the first-choice equipment for many scientists when it comes to recording brain waves for research purposes. On one hand, this is perfectly understandable due to its availability and relatively low cost (especially in comparison to some clinical-level EEG devices), but, on the other hand, quality of the recorded signals is gradually increasing and reaching levels that were offered just a few years ago by much more expensive devices used in medicine for diagnostic purposes. In many cases, a well-designed filter and/or a well-thought signal acquisition method improve the signal quality to the level that it becomes good enough to become subject of further analysis allowing to formulate some valid scientific theories and draw far-fetched conclusions related to human brain operation. In this paper, we propose a smoothing filter based upon the Savitzky–Golay filter for the purpose of EEG signal filtering. Additionally, we provide a summary and comparison of the applied filter to some other approaches to EEG data filtering. All the analyzed signals were acquired from subjects performing visually involving high-concentration tasks with audio stimuli using Emotiv EPOC Flex equipment.

The article presents an application of Prony’s method with some known components in the analysis of electric power quality. Modifications of the Prony algorithm broaden the scope of method application. Modification of the filter of known components enables more accurate analysis of the parameters of unknown components and components with known or assumed frequencies. This article presents a comparison of the results of analyses conducted with the proposed algorithm for simulated and real signals and the results obtained by means of a commercial electric power quality testing device, operating in class A and using the Fourier transform. The proposed method enables to estimate the levels of the harmonic components, the frequency of the fundamental signal and real parameters of the interharmonic components, which are grouped and averaged in the contemporary monitoring equipment. Knowledge of the individual parameters of the interharmonics has considerable diagnostic importance while removing causes of incorrect operation affecting sensitive equipment in some electric power systems. Additionally, the algorithm is capable of analyzing exponentially damped components and finds its application in analysis of disturbances, for example, transient oscillations.

Short Time Algorithm of Power Waveforms Fundamental Harmonic Estimation With Use of Prony's Methods: This paper presents an example of practical use of Prony's method for monitoring of power waveform fundamental harmonic fluctuations, which is required for the analysis of window synchronizations in frequency analyses in power monitoring systems. The example presented offers verification of the authors' theoretical considerations published earlier in articles about Prony's method and its opportunities for practical use for real life signals. The investigations shown are based on the least squares Prony's method, which, in connection with digital filtrations, enables estimations of fundamental frequency at the rate of even tens of times per one fundamental harmonic period.