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Abstract

A traditional frequency analysis is not appropriate for observation of properties of non-stationary signals. This stems from the fact that the time resolution is not defined in the Fourier spectrum. Thus, there is a need for methods implementing joint time-frequency analysis (t/f) algorithms. Practical aspects of some representative methods of time-frequency analysis, including Short Time Fourier Transform, Gabor Transform, Wigner-Ville Transform and Cone-Shaped Transform are described in this paper. Unfortunately, there is no correlation between the width of the time-frequency window and its frequency content in the t/f analysis. This property is not valid in the case of a wavelet transform. A wavelet is a wave-like oscillation, which forms its own “wavelet window”. Compression of the wavelet narrows the window, and vice versa. Individual wavelet functions are well localized in time and simultaneously in scale (the equivalent of frequency). The wavelet analysis owes its effectiveness to the pyramid algorithm described by Mallat, which enables fast decomposition of a signal into wavelet components.
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Abstract

In the last decade of the XX-th century, several academic centers have launched intensive research programs on the brain-computer interface (BCI). The current state of research allows to use certain properties of electromagnetic waves (brain activity) produced by brain neurons, measured using electroencephalographic techniques (EEG recording involves reading from electrodes attached to the scalp - the non-invasive method - or with electrodes implanted directly into the cerebral cortex - the invasive method). A BCI system reads the user's “intentions” by decoding certain features of the EEG signal. Those features are then classified and "translated" (on-line) into commands used to control a computer, prosthesis, wheelchair or other device. In this article, the authors try to show that the BCI is a typical example of a measurement and control unit.
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