Time-frequency Approximations Research Articles

Characteristic of Mayer Waves in Electrophysiological, Hemodynamic and Vascular Signals.

We evaluated the properties of oscillations in the Mayer waves (MW) frequency range (Hz) detected in blood pressure, heart rate variability, cerebral blood oxygenation changes and evolution of electroencephalographic (EEG) rhythms to elucidate the mechanisms of MW generation. We examined the persistence of MW in different signals and stability of their oscillations on the level of individual MW waveforms, which was achieved by applying matching pursuit (MP). MP yields adaptive time-frequency approximation of signal's structures in terms of frequency, amplitude, time occurrence, and time-span. The number of waveforms contributing to 95% of the energy of the signals was vastly different for the time series, but the average number of waveforms conforming to the MW criteria was almost the same ( per 120s epoch). In all the investigated signals, MW had the same distributions of frequency and the number of cycles. We show that the MW energy ratios in different signals varied strongly, . The highest percentage of MW energy was observed in blood pressure signals, heart rate variability, and reduced hemoglobin, in contrast to brain signals and oxygenated hemoglobin. The percentage of MW energy was related to the strength of causal influence exerted by them on the other signals. Our results indicate existence of a common mechanism of MW generation and support the hypothesis of MW generation in the baroreflex loop; however, they do not exclude the action of a central pacemaker.

Explicit parameterization of sleep EEG transients

Adaptive time-frequency approximations, implemented via the matching pursuit algorithm, offer description of local signals structures in terms of their time occurrence and width, frequency and amplitude. This allows to construct explicit filters for finding EEG waveforms, known from the visual analysis, in the matching pursuit decomposition of signals. In such a way detectors of relevant structures of both transient and oscillatory nature can be constructed in the space of physically meaningful parameters. This study presents evaluation of changes of power and frequency of sleep spindles and delta waves, related to the depth of the sleep, which were previously assessed in a qualitative way. We confirm quantitatively the decrease of frequencies of sleep spindles and delta waves with the depth of the sleep.

Micro- and macrostructure of sleep EEG

Electroencephalogram (EEG) provides important and unique information about the sleeping brain. Polysomnography was the major method of sleep analysis and the main diagnostic tool in sleep medicine. The standard interpretation of polysomnographic recordings describes their macrostructure in terms of sleep stages, delineated according to R&K scoring criteria. Several descriptors of sleep microstructure rely on the quantification of sleep spindles and slow wave activities, detection of arousals, etc. However, these descriptors are usually assessed by means of substantially different signal processing (or visual) methods. This hinders possibilities of combining their results into a coherent description of the sleep process. This study proposes a solution to these problems in terms of a framework based upon adaptive time-frequency approximations - a recent, advanced method of signal processing. The proposed approach provides compatibility with the visual EEG analysis and standard definitions of EEG structures and describes both the macro- and microstructure of sleep EEG. Adaptive time-frequency approximations of signals calculated by means of the matching pursuit (MP) algorithm allow for the discrimination between series of unrelated structures and oscillatory activity. The detection, parametrization, and description of all these features of sleep are based upon the same unifying approach

Signal analysis and weighted polynomial approximation

We present applications of Hermite polynomials in signal analysis. Among other result, we give a characterization of the so-called time-frequency window functions in terms of the Hermite--Fourier coefficients, a Bernstein-type theorem for the best approximations of window functions by Hermite-functions, time-frequency approximations. Some analogues for Hankel-transforms will also be considered.

On the methodological unification in electroencephalography

BackgroundThis paper presents results of a pursuit of a repeatable and objective methodology of analysis of the electroencephalographic (EEG) time series.MethodsAdaptive time-frequency approximations of EEG are discussed in the light of the available experimental and theoretical evidence, and applicability in various experimental and clinical setups.ResultsFour lemmas and three conjectures support the following conclusion.ConclusionAdaptive time-frequency approximations of signals unify most of the univariate computational approaches to EEG analysis, and offer compatibility with its traditional (visual) analysis, used in clinical applications.

Adaptive time-frequency parametrization of epileptic spikes.

Adaptive time-frequency approximations of signals have proven to be a valuable tool in electroencephalogram (EEG) analysis and research, where it is believed that oscillatory phenomena play a crucial role in the brain's information processing. This paper extends this paradigm to the nonoscillating structures such as the epileptic EEG spikes, and presents the advantages of their parametrization in general terms such as amplitude and half-width. A simple detector of epileptic spikes in the space of these parameters, tested on a limited data set, gives very promising results. It also provides a direct distinction between randomly occurring spikes or spike/wave complexes and rhythmic discharges.

Identification of otoacoustic emissions components by means of adaptive approximations.

Clicks and a set of tone bursts covering the same frequency band were applied as a stimuli evoking otoacoustic emissions (OAE). Recorded otoacoustic emissions were decomposed into the basic waveforms by means of high-resolution adaptive time-frequency approximation method based on the matching pursuit algorithm. The method allows for description of the signal components in terms of frequencies, time occurrences, time spans, and energy. The analysis of OAE's energy density distributions in time-frequency space revealed that click responses can be considered as linear superpositions of responses to tone bursts, The frequency-latency relationship was studied and compared with earlier works. The method made possible the exhaustive description of the resonant modes specific for given subject/ear. They were characterized not only by the close frequencies appearing for different tones, but they usually had similar latencies and time spans. Short-time and long-time resonant modes were identified. The second ones might be connected with spontaneous emissions. The method opens new perspectives in studying the fine structure of the OAE and testing of the theoretical models.

A unified time-frequency parametrization of EEGs.

Seventy years since the first recording of the human electroencephalogram (EEG), visual analysis of raw EEG traces is still the major clinical tool and point of reference for other methods, in spite of its inherent limitations: low repeatability and high cost. Seven years since the introduction of the matching pursuit (MP) algorithm, the authors have collected evidence suggesting that adaptive time-frequency approximation is a good candidate for a universal high-resolution parameterization of EEG data, compatible with the visual and spectral analysis, and applicable to a large class of problems. Here, the authors briefly discuss the need for a generally applicable method for a mathematical description (parameterization) of the signal, which would be directly related to the heritage of the traditional EEG analysis. In this context the authors discuss application of the MP algorithm. They present recent advances in analysis of sleep EEGs and discuss earlier works on event-related potentials and epileptic recordings.