This paper presents a summary of time-frequency analysis of the electrical activity of the brain (EEG). conservation: For a complete dictionary the procedure converges to f: From this equation we can derive a time-frequency distribution of the signal’s energy, that is free of cross-terms, by adding Wigner distributions of selected functions: This magnitude is presented in Figure ?Figure7,7, buy Freselestat calculated from MP decomposition of a simulated signal with known and simple content. We observe that most of the structures are represented compactly and with high resolution, except for the structure of changing frequency (linear chirp). It is represented by a series of structures of constant frequency, since in the applied Gabor dictionary (section 5) we have only constant frequency modulations. Section 7 presents an alternative approach to this issue. Figure 7 Time-frequency map of energy density of a 500-points simulated signal (e) composed of four sine-modulated Gaussians, i.e. Gabor functions (a-b), sine wave and one-point discontinuity (c) and sine wave with linear frequency modulation-chirp (d). Distribution … Figure ?Figure88 presents estimates of the time-frequency density of the same signal’s energy, obtained from: spectrograms with different window widths, continuous wavelet transform and smoothed pseudo Wigner-Ville distribution. Only in the last case Rabbit polyclonal to COPE representation of the chirp looks better than on the plot obtained from MP decomposition, but we must take into account that in this case the parameters of the kernel of the distribution were optimized for this particular signal. buy Freselestat Except for the lack of cross terms and high resolution, adaptive time-frequency parametrizations exhibit one buy Freselestat more basic and important advantage over buy Freselestat the continuous time-frequency representations. Unlike the maps from Figure ?Figure8,8, for all the structures presented in Figure ?Figure77 we have a priori the exact values of their time and frequency centers, widths, amplitudes and phases. This property will be thoroughly explored in the following studies. First application in EEG analysis: sleep spindles The presence of sleep spindle should not be defined unless it is of at least 0.5 sec duration, i.e., one should be able to count 6 or 7 distinct waves within the half-second period. (…) The term should be used only to describe activity between 12 and 14 cps. C says the definition from the basic reference  C “A manual of standardized terminology, techniques and scoring system for sleep stages in human subjects”. It can be directly translated into the language of parameters of the structures fitted to the signal by the algorithm discussed in the previous section. By choosing from the time-frequency atoms, fitted to EEG by the MP algorithm, those conforming to the above criteria, we obtain a detailed, automatic and high-resolution parametrization of the relevant structures, which correspond to sleep spindles [9,10]. Figures ?Figures1010 and ?and1111 present results of such a procedure carried out for several derivations of an overnight sleep EEG recording. This parametrization has proven to be consistent with visual detection, especially for the structures of higher amplitudes . For lower amplitudes the algorithm detects also spindles elusive to a human expert. Figure 10 Histograms of frequencies of sleep spindles detected in one overnight EEG recording. Plots are placed on page according to relative positions of corresponding derivations from the 10C20 system C front of head towards the top of page Figure 11 Amplitudes of detected spindles (vertical) plotted versus their frequencies (horizontal) for the same data and derivations as Fig ?Fig1010 Figure 9 Time-frequency energy distribution (equation 5) of 20 seconds of sleep EEG; structures corresponding to.