186 research outputs found
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
Optimal filtering in fractional fourier domains
For time-invariant degradation models and stationary signals and noise, the classical Fourier domain Wiener filter, which can be implemented in O(NlogN) time, gives the minimum mean-square-error estimate of the original undistorted signal. For time-varying degradations and nonstationary processes, however, the optimal linear estimate requires O(N2) time for implementation. We consider filtering in fractional Fourier domains, which enables significant reduction of the error compared with ordinary Fourier domain filtering for certain types of degradation and noise (especially of chirped nature), while requiring only O(N\og N) implementation time. Thus, improved performance is achieved at no additional cost. Expressions for the optimal filter functions in fractional domains are derived, and several illustrative examples are given in which significant reduction of the error (by a factor of 50) is obtained. © 1997 IEEE
Recent advances in theory and methods for nonstationary signal analysis
[No abstract available
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