Recent Advances in Theory and Methods for Nonstationary Signal Analysis

Cataloged from PDF version of article.All physical processes are nonstationary. When analyzing time series, it should be remembered that nature can be amazingly complex and that many of the theoretical constructs used in stochastic process theory, for example, linearity, ergodicity, normality, and particularly stationarity, are mathematical fairy tales. There are no stationary time series in the strict mathematical sense; at the very least, everything has a beginning and an end. Thus, while it is necessary to know the theory of stationary processes, one should not adhere to it dogmatically when analyzing data from physical sources, particularly when the observations span an extended period. Nonstationary signals are appropriate models for signals arising in several fields of applications including communications, speech and audio, mechanics, geophysics, climatology, solar and space physics, optics, and biomedical engineering. Nonstationary models account for possible time variations of statistical functions and/or spectral characteristics of signals. Thus, they provide analysis tools more general than the classical Fourier transform for finite-energy signals or the power spectrum for finite-power stationary signals. Nonstationarity, being a “nonproperty” has been analyzed from several different points of view. Several approaches that generalize the traditional concepts of Fourier analysis have been considered, including time-frequency, time-scale, and wavelet analysis, and fractional Fourier and linear canonical transforms

Recent Advances in Theory and Methods for Nonstationary Signal Analysis

Cataloged from PDF version of article.All physical processes are nonstationary. When analyzing time series, it should be remembered that nature can be amazingly complex and that many of the theoretical constructs used in stochastic process theory, for example, linearity, ergodicity, normality, and particularly stationarity, are mathematical fairy tales. There are no stationary time series in the strict mathematical sense; at the very least, everything has a beginning and an end. Thus, while it is necessary to know the theory of stationary processes, one should not adhere to it dogmatically when analyzing data from physical sources, particularly when the observations span an extended period. Nonstationary signals are appropriate models for signals arising in several fields of applications including communications, speech and audio, mechanics, geophysics, climatology, solar and space physics, optics, and biomedical engineering. Nonstationary models account for possible time variations of statistical functions and/or spectral characteristics of signals. Thus, they provide analysis tools more general than the classical Fourier transform for finite-energy signals or the power spectrum for finite-power stationary signals. Nonstationarity, being a “nonproperty” has been analyzed from several different points of view. Several approaches that generalize the traditional concepts of Fourier analysis have been considered, including time-frequency, time-scale, and wavelet analysis, and fractional Fourier and linear canonical transforms

Recent advances in theory and methods for nonstationary signal analysis

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Neurological and Mental Disorders

Mental disorders can result from disruption of neuronal circuitry, damage to the neuronal and non-neuronal cells, altered circuitry in the different regions of the brain and any changes in the permeability of the blood brain barrier. Early identification of these impairments through investigative means could help to improve the outcome for many brain and behaviour disease states.The chapters in this book describe how these abnormalities can lead to neurological and mental diseases such as ADHD (Attention Deficit Hyperactivity Disorder), anxiety disorders, Alzheimer’s disease and personality and eating disorders. Psycho-social traumas, especially during childhood, increase the incidence of amnesia and transient global amnesia, leading to the temporary inability to create new memories.Early detection of these disorders could benefit many complex diseases such as schizophrenia and depression