% Bibliography of Spectral and Time-Series Analysis: % Recent and Novel Techniques % % Last Updated: 2/10/96 % % This is a bibliography of papers, books, etc. that provide % sources of information for recently developed or novel techniques % in spectral or time-series analysis of time series from linear % and nonlinear systems. It ranges from the papers of % David Thomson et al. on the multiple-data-window technique to % the singular spectrum analysis method to various papers on % aspects of time-frequency representations, i.e. wavelets, % chirplets, fractional Fourier transformations, Gabor transforms, % the Wigner distribution, etc. Also included are documents % about higher-order time series analysis and the analysis % of chaotic data from nonlinear systems. %
%AAAA
@article{abarbanel-brown-etal:1993,
Author = "Abarbanel, H. D. I. and R. Brown and J. J. Siderowich and
L. S. Tsimring",
Title = "The analysis of observed chaotic data in physical systems",
Journal = "Rev. Mod. Phys.",
Volume = "65",
Year = "1993",
Pages = "1331--1392",
Abstract = "Chaotic time series data are observed routinely in
experiments on physical systems and in observations in the field.
The authors review developments in the extraction of information
of physical importance from such measurements. They discuss
methods for (1) separating the signal of physical interest
from contamination (``noise reduction''), (2) constructing an
appropriate state space or phase space for the data in which the
full structure of the strange attractor associated with the
chaotic observations is unfolded, (3) evaluating invariant
properties of the dynamics such as dimensions, Lyapunov exponents,
and topological characteristics, and (4) model making, local and
global, for prediction and other goals. They briefly touch on the
effects of linearly filtering data before analyzing it as a chaotic
time series. The emphasis throughout the review is on the tools
one now has for the realistic study of measured data in laboratory
and field settings. It is the goal of this review to bring these
tools into general use among physicists who study classical and
semiclassical systems. Much of the progress in studying chaotic
systems has rested on computational tools with some underlying
rigrous mathematics. Heuristic and intuitive analysis tools guided
by the mathematics and realizable on existing computers constitute
the core of this review.",
Note = "
\begin{enumerate}
\item Introduction,
\begin{enumerate}
\item Observed chaos,
\item Outline of the review,
\end{enumerate}
\item Signals, dynamical systems, and chaos,
\item Analyzing measured signals--linear and nonlinear,
\begin{enumerate}
\item Signal separation,
\item Finding the space,
\item Classification and identification,
\item Modeling--linear and nonlinear,
\item Signal synthesis,
\end{enumerate}
\item Reconstructing phase space or state space,
\begin{enumerate}
\item Choosing time delays,
\item Average mutual information,
\item Choosing the embedding dimension,
\item T and d_E,
\end{enumerate}
\item Invariants of the dynamics,
\begin{enumerate}
\item Density estimation,
\item Dimensions,
\item A seque--from geometry to dynamics,
\item Lyapunov spectrum,
\item Global exponents,
\item Ideal case: Known dynamics,
\item Real world: Observations,
\item Local exponents from known dynamics and from observations,
\item Topological invariants,
\end{enumerate}
\item Nonlinear model building: Prediction in chaos,
\begin{enumerate}
\item The dimension of models,
\item Local modeling,
\item Global modeling,
\item In between local and global modeling,
\end{enumerate}
\item Signal separation--'noise reduction',
\begin{enumerate}
\item Knowing the dynamics: manifold decomposition,
\item Knowing a signal: probabilistic cleaning,
\item Knowing very little,
\end{enumerate}
\item Linearly filtered signals,
\item Control and synchronization of chaotic systems,
\begin{enumerate}
\item Controlling chaos,
\item Synchronization and chaotic driving,
\end{enumerate}
\item Spatio-temporal chaos,
\item Conclusions,
\begin{enumerate}
\item Summary,
\item Cloudy crystal ball gazing
\end{enumerate}
\end{enumerate}" }
%BBBB
@article{bradshaw-mcintosh:1994,
Author = "Bradshaw, G. A. and B. A. McIntosh",
Title = "Determining climate--induced patterns using wavelet analysis",
Journal = "Environmental Pollution",
Volume = "83",
Year = "1994",
Pages = "133--142",
Abstract = "A method using wavelet analysis is introduced for the
purpose of identifying and isolating inferred climatic components
of the hydrologic record. This method affords an informed procedure
for choosing filter dimensions for the purpose of signal decomposition." }
%CCCC
@article{chave-thomson-etal:1987,
Author = "Chave, Alan D. and David J. Thomson and Mark E. Ander",
Title = "On the robust estimation of power spectra, coherences and
transfer functions",
Journal = "JGR",
Volume = "92",
Year = "1987",
Pages = "633--648",
Abstract = "Robust estimation of power spectra, coherences, and transfer
functions is investigated in the context of geophysical data processing.
The methods described are frequency-domain extensions of current
techniques from the statistical literature and are applicable in
cases where section-averaging methods would be used with data that
are contaminated by local nonstationarity or isolated outliers.
The paper begins with a review of robust estimation theory,
emphasizing statistical principles and the maximum likelihood or
M-estimators. These are combined with section-averaging spectral
techniques to obtain robust estimates of power spectra, coherences,
and transfer functions in an automatic, data-adaptive fashion.
Because robust methods implicitly identify abnormal data, methods
for monitoring the statistical behavior of the estimation process
using quantile-quantile plots are also discussed. The results are
illustrated using a variety of examples from electromagnetic
geophysics." }
@article{cohen.l:1989,
Author = "Cohen, L.",
Title = "Time--frequency distributions -- A review",
Journal = "Proc. IEEE",
Volume = "77",
Year = "1989",
Pages = "941--981",
Abstract = "A review and tutorial of the fundamental ideas and methods of
joint time--frequency distributions is presented. The objective of
the field is to describe how the spectral content of a signal is changing
in time, and to develop the mathematical and physical ideas needed to
understand what a time--varying spectrum is. The basic goal is to devise
a distribution that represents the energy or intensity of a signal
simultaneously in time and frequency. Although the basic notions
have been developing steadily over the last 40 years, there have
recently been significant advances. Thsi review is presented to be
understandable to the nonspecialist with emphasis on the diversity
of concepts and motivations that have gone into the formation of
the field." }
%DDDD
@incollection{davis-marshak-etal:1994,
Author = "Davis, Anthony and Alexander Marshak and Warren Wiscombe",
Title = "Wavelet-based multifractal analysis of non-stationary
and/or intermittent geophysical signals",
Booktitle = "Wavelets in Geophysics",
Editor = "Efi Foufoula-Georgiou and Praveen Kumar",
Publisher = "Academic Press",
Year = "1994",
Pages = "249--298",
Keyword = "wavelets, fractals, signal processing",
Abstract = "This shows how wavelet transforms can be used to compute
simple yet dynamically meaningful statistical properties of a
one-dimensional data set representative of a geophysical field or
time-series. This paper is available via anonymous ftp at
ftp://climate.gsfc.nasa.gov/pub/marshak/Wavelets.paper/wavelets.text.PS.Z
(99,067) with the figures in wavelets.figs.PS.Z (399,610)." }
%EEEE
%FFFF
%GGGG
@article{gardner:1991,
Author = "Gardner, William A.",
Title = "Exploitation of spectral redundancy in cyclostationary signals",
Journal = "IEEE Signal Processing Magazine",
Year = "1991",
Month = "apr",
Pages = "14--36",
Abstract = "Three properties shared by many manmade signals are
described: (1) the property that enables generation of spectral
lines by quadratically transforming the signal; (2) the statistical
property called second-order {\it cyclostationarity}, which means
that the autocorrelation function fluctuates periodically with
time; and (3) the correlation property for signal components in
distinct spectral bands. It is shown that these three properties
are different manifestations of a single attribute called
{\it spectral redundancy}. This intriguing attribute is studied,
and a variety of ways for exploiting it to perform signal
processing tasks involving detection and estimation of highly
corrupted manmade signals are explained." }
%HHHH
@article{haykin-li:1995,
Author = "Haykin, Simon and Xiao Bo Li",
Title = "Detection of signals in chaos",
Journal = "Proc. IEEE",
Volume = "83",
Year = "1995",
Pages = "95--122",
Abstract = "A new method for the detection of signals in ``noise''
is presented. It is based on the premise that the ``noise'' is
chaotic with at least one positive Lyapunov exponent. The method
is naturally rooted in nonlinear dynamical systems and relies on
neural networks for its implementation.
First presented is an introductory review of chaos emphasizing
experimental studies of chaos using a time series. Specifically
discussed are the issues involved in the reconstruction of chaotic
dynamics, attractor dimensions, and Lyapunov exponents. Procedures
for the estimation of the correlation dimension and the largest
Lyapunov exponent are described, and the need for an adequate
data length stressed. The second part of the paper applies the
method to an example of the radar detection of a small target
in sea clutter in excruciating detail." }
%IIII
%JJJJ
%KKKK
@article{kleiner-martin-etal:1979,
Title = "Robust estimation of power spectra (with discussion)",
Author = "Kleiner, B. and R. D. Martin and D. J. Thomson",
Journal = "J. R. Stat. Soc. Ser. B",
Volume = "41",
Year = "1979",
Pages = "313--351" }
@article{kuo.c-lindberg-etal:1990,
Author = "Kuo, Cynthia and Craig Lindberg and David J. Thomson",
Title = "Coherence established between atmospheric carbon dioxide
and global temperature",
Journal = "Nature",
Volume = "343",
Year = "1990",
Pages = "709--714",
Abstract = "The hypothesis that the increase in atmospheric carbon
dioxide is related to observable changes in the climate is tested
using modern methods of time-series analysis. The results confirm
that average global temperature is increasing, and that temperature
and atmospheric carbon dioxide are significantly correlated over the
past thirty years. Changes in carbon dioxide content lag those
in temperature by five months." }
%LLLL
@article{landau-pollak:1961,
Author = "Landau, H. J. and H. O. Pollak",
Title = "Prolate spheroidal wave functions, Fourier analysis and
uncertainty - II",
Journal = "Bell Syst. Tech. J.",
Volume = "40",
Year = "1961",
Pages = "65--84" }
@article{lau-weng:1995,
Author = "Lau, K.-M. and Hengyi Weng",
Title = "Climate signal detection using wavelet transform: How to
make a time series sing",
Journal = "BAMS",
Volume = "76",
Year = "1995",
Pages = "2391--2402",
Abstract = "The application of the wavelet transform (WT) to climate time
series analyses is introduced. A tutorial description of the basic
concept of WT, compared with similar concepts used in music, is also
provided (whence the title). Using an analogy between WT representation
of a time sereis and a music score, the authors illustrate the
importance of local versus global information in the time-frequency
localization of climate signals. Examples of WT applied to climate data
analysis are demonstrated using analytic signals as well as real
climate time series. Results of WT applied to two climate time
series--that is, a proxy paleoclimate time series with a 2.5-Myr
deep-sea sediment record of delta O18 and a 140-yr monthly record of
Northern Hemisphere surface temperature--are presented. The former
shows the presence of a 40-kyr and a 100-kyr oscillation and an
abrupt transition in the oscillation regime at 0.7 Myr before the
present, consistent with previous studies. The latter possesses
a myriad of oscillatory modes from interannual (2-5 yr),
interdecadal (10-12 yr, 20-25 yr, and 40-60 yr), and
century (180 yr) scales at different periods of the data record.
In spite of the large difference in timescales, common features
in time-frequency characteristics of these two time series have
been identified. These features suggest that the variations of
the earth's climate are consistent with those exhibited by a nonlinear
dynamical system under external forcings." }
@article{lindberg-park:1987,
Author = "Lindberg, C. R. and J. Park",
Title = "Multiple-taper spectral analysis of terrestrial free
oscillations: Part II",
Journal = "Geophysical Journal R. Astron. Soc.",
Volume = "91",
Year = "1987",
Pages = "795--836" }
%MMMM
@article{maragos:1995,
Title = "Slope transforms: Theory and application to nonlinear
signal processing",
Author = "Maragos, Petros",
Journal = "IEEE Trans. Sig. Proc.",
Volume = "43",
Year = "1995",
Pages = "864--877" }
@article{martin.r-thomson:1982,
Title = "Robust-resistant spectrum estimation",
Author = "Martin, R. D. and D. J. Thomson",
Journal = "Proc. IEEE",
Volume = "70",
Year = "1982",
Pages = "1097--1115" }
@article{mendel:1991,
Author = "Mendel, Jerry M.",
Title = "Tutorial on higher-order statistics (spectra) in signal
processing and system theory: Theoretical results and some
applications",
Journal = "Proc. IEEE",
Volume = "79",
Year = "1991",
Pages = "278--305",
Abstract = "During the past few years there has been an increasing
interest in applying higher-order statistics to a wide range of
signal processing and system theory problems. These statistics
are very useful in problems where either non-Gaussianity,
nonmimimum phase, colored noise, or nonlinearities are important
and must be accounted for. More than 200 papers have already been
published. These papers contain both theoretical and algorithmic
results. The purpose of the present tutorial paper is twofold,
namely: 1) to collect what this author believes to be some of the
most useful theoretical results in one place (they are presently
scattered in many papers), thereby making them readily accessible
to readers for the first time and, 2) to describe the applications
of higher-order statistics to the identification of (possibly)
nonminimum phase channels from just noisy output measurements." }
@incollection{mullis-scharf:1991,
Author = "Mullis, C. T. and L. L. Scharf",
Title = "Quadratic estimators of the power spectrum",
Booktitle = "Advances in Spectrum Analysis and Array Processing",
Editor = "S. Haykin",
Publisher = "Prentice-Hall",
Year = "1991",
Pages = "1--57" }
%NNNN
@article{nikias-mendel:1993,
Author = "Nikias, Chrysostomos L. and Jerry M. Mendel",
Title = "Signal processing with higher-order spectra",
Journal = "IEEE Signal Processing Magazine",
Year = "1993",
Month = "jul",
Pages = "10--37",
Abstract = "The estimation of the power spectrum of discrete-time
signals has been a useful digital signal processing tool for
over 30 years, although the information contained in the power
spectrum is essentially that which is present in the autocorrelation
sequence. This suffices for the description of a Gaussian signal,
but in many practical situations we need to extract information
regarding deviations from Gaussianity and phase relations.
Higher order spectra (also known as polyspectra) do contain
such information. Particular cases of higher order spectra include
the bispectrum and the trispectrum which are the Fourier transforms
of, respectively, the third- and fourth-order statistics.
Motivations behind the use of higher order spectra include
techniques to: (1) suppress additive colored Gaussian noise
of unknown power spectra; (2) identify non-minimum phase systems
or reconstruct nonminimum phase signals; (3) extract information
due to deviations from Gaussianity; and (4) detect and characterize
nonlinear properties in signals as well as identify nonlinear
systems." }
@book{nikias-petropulu:1993,
Author = "Nikias, Chrysostomos L. and Athina P. Petropulu",
Title = "Higher-Order Spectra Analysis: A Nonlinear Signal Processing
Framework",
Publisher = "PTR Prentice-Hall",
Year = "1993",
Pages = "537",
LOC = "TK 5102.9 N54 1993",
ISBN = "0-13-678210-8",
Note = "
\begin{enumerate}
\item Introduction
\begin{enumerate}
\item Power spectrum
\item Why polyspectra in signal processing?
\item Applications
\end{enumerate}
\item Cumulant spectra of stochastic signals
\begin{enumerate}
\item Introduction
\item Moments and cumulants
\item Cumulant spectra
\item Cumulant spectra of non-Gaussian linear processes
\item Detecting and identifying nonlinear processes
\item Summary
\end{enumerate}
\item Moment spectra of deterministic signals
\begin{enumerate}
\item Introduction
\item Moments of energy signals
\item Moment spectra of aperiodic energy signals
\item Moments of power signals
\item Moment spectra of periodic power signals
\item Summary
\end{enumerate}
\item Conventional methods for the estimation of higher-order
spectra
\begin{enumerate}
\item Introduction
\item Indirect class of conventional methods
\item Direct class of conventional methods
\item Complex demodulates class of conventional methods
\item Statistical properties of conventional methods
\item Test for aliasing with the bispectrum
\item Bispectrum computation on polar rasters
\item Summary
\end{enumerate}
\item Higher-order cepstra (polycepstra)
\begin{enumerate}
\item Introduction
\item The complex cepstrum of deterministic energy signals
\item The differential cepstrum of deterministic energy
signals
\item The power cepstrum of deterministic and stochastic
signals
\item The bicepstrum and tricepstrum of deterministic
and stochastic signals
\item The cepstrum of bicoherency
\item Higher-order spectrum factorization and index for
linearity
\item Inverse filter reconstruction
\item The cross-bicepstrum of deterministic and stochastic
signals
\item Analytic performance evaluation of the complex
cepstrum and bicepstrum
\item Summary
\end{enumerate}
\item Nonparametric methods for signal recovery from higher-order
spectra
\begin{enumerate}
\item Introduction
\item Magnitude and phase estimation from higher-order
spectra
\item Phase recovery algorithms
\item Phase and magnitude algorithms based on
polyspectra/polycepstra properties
\item Signal reconstruction from only the phase of the
bispectrum
\item Signal reconstruction from the bispectrum based on
the method of POCs
\item Blind deconvolution using BIRA
\item Summary
\end{enumerate}
\item Parametric methods for the estimation of higher-order
spectra
\begin{enumerate}
\item Introduction
\item MA methods
\item Noncausal AR methods
\item ARMA methods
\item Model order determination
\item Summary
\end{enumerate}
\item Direction of arrival estimation and analysis of transient
signals
\begin{enumerate}
\item Introduction
\item Time delay estimation
\item Bearing estimation with higher-order statistics
\item Parameter estimation of transient signals
\item Detection of transient signals
\item Summary
\end{enumerate}
\item Adaptive filtering with higher-order statistics
\begin{enumerate}
\item Introduction
\item Adaptive filtering with second-order statistics
\item The LMF and RLF algorithm
\item Adaptive HR algorithms based on HOS
\item Adaptive lattice linear prediction using cumulants
\item Adaptive MA model estimation via noncausal AR
approximations
\item Adaptive time delay estimation
\item Adaptive blind equalization algorithms
\item Summary
\end{enumerate}
\item Detection and characterization of nonlinearities in
time series
\begin{enumerate}
\item General Volterra systems
\item Second-order Volterra filters
\item The identification of a particular nonlinear
time series system
\item Quadratic phase coupling
\item Cubic phase coupling
\item Summary
\end{enumerate}
\item Time-frequency distributions based on higher-order
spectra
\begin{enumerate}
\item Introduction
\item Wigner-Ville distribution (WD)
\item Cohen's general class of time-frequency distributions
\item Wigner higher-order moment spectra: Continuous case
\item Wigner polyspectra: Discrete case
\item Applications of Wigner higher-order spectra
\item Summary
\end{enumerate}
\item Current and future trends
\end{enumerate}" }
%OOOO
@article{ozaktas-barshan-etal:1994,
Author = "Ozaktas, Haldun M. and Billur Barshan and David Mendlovic and
Levent Onural",
Title = "Convolution, filtering, and multiplexing in fractional Fourier
domains and their relation to chirp and wavelet transforms",
Journal = "J. Opt. Soc. Am. A",
Volume = "11",
Year = "1994",
Pages = "547--559",
Keyword = "Fourier transforms, fractinal Fourier transforms, wavelets,
chirplets",
Abstract = "A concise introduction to the concept of fractional Fourier
transforms is followed by a discussion of their relation to chirp and
wavelet transforms. The notion of fractional Fourier domains is
developed in conjunction with the Wigner distribution of a signal.
Convolution, filtering, and multiplexing of signals in fractional
domains are discussed, revealing that under certain conditions one can
improve on the special cases of these operations in the conventional
space and frequency domains." }
%PPPP
@article{park.j-lindberg-etal:1987a,
Title = "Multiple-taper spectral analysis of terrestrial free
oscillations: part I",
Author = "Park, J. and C. R. Lindberg and D. J. Thomson",
Journal = "Geophys. J. R. Astr. Soc.",
Volume = "91",
Year = "1987",
Pages = "755--794" }
@article{park.j-lindberg-etal:1987b,
Title = "Multitaper spectral analysis of high-frequency seismograms",
Author = "Park, J. and C. R. Lindberg and F. L. Vernon III",
Journal = "J. Geophys. Res.",
Volume = "92",
Year = "1987",
Pages = "12,675--12,684" }
%QQQQ
%RRRR
@article{roberts.r-brown-etal:1991,
Author = "Roberts, Randy S. and William A. Brown and Herschel H. Loomis, Jr.",
Title = "Computationally efficient algorithms for cyclic spectral analysis",
Journal = "IEEE Signal Processing Magazine",
Year = "1991",
Month = "apr",
Pages = "38--49",
Abstract = "Two computationally efficient algorithms for digital
cyclic spectral analysis, the FFT Accumulation Method (FAM) and
the Strip SPectral Correlation Algorithm (SSCA) are developed from
a series modifications on a simple time smoothing algorithm. The
signal processing, computational, and structural attributes of time
smoothing algorithms are presented with emphasis on the FAM and
SSCA." }
@article{rioul-vetterli:1991,
Author = "Rioul, O[livier]. and M. Vetterli",
Title = "Wavelets and signal processing",
Journal = "IEEE Signal Processing Magazine",
Year = "1991",
Month = "oct",
Pages = "14--37" }
%SSSS
@article{slepian:1964,
Author = "Slepian, D.",
Title = "Prolate spheroidal wave functions, Fourier analysis, and
uncertainty - IV. Extensions to many dimensions; generalized
prolate spheroidal functions",
Journal = "Bell Syst. Tech. J.",
Volume = "43",
Year = "1964",
Pages = "3009--3058" }
@article{slepian:1978,
Author = "Slepian, D.",
Title = "Prolate spheroidal wavefunctions, Fourier analysis, and
uncertainty - V. The discrete case",
Journal = "Bell Syst. Tech. J.",
Volume = "57",
Year = "1978",
Pages = "1371--1429" }
@article{slepian-pollak:1961,
Author = "Slepian, D. and H. O. Pollak",
Title = "Prolate spheroidal wavefunctions, Fourier analysis, and
uncertainty - I",
Journal = "Bell Syst. Tech. J.",
Volume = "40",
Year = "1961",
Pages = "43--64" }
@article{slepian-pollak:1962,
Author = "Slepian, D. and H. O. Pollak",
Title = "Prolate spheroidal wave functions, Fourier analysis, and
uncertainty - III. The dimension of essentially time- and band-limited
signals",
Journal = "Bell Syst. Tech. J.",
Volume = "41",
Year = "1962",
Pages = "1295--1336" }
@article{strang:1993,
Author = "Strang, Gilbert",
Title = "Wavelet transforms versus Fourier transforms",
Journal = "Bull. (New Series) AMS",
Volume = "28",
Year = "1993",
Pages = "288--305",
Abstract = "This is a very basic introduction to wavelets. Wavelets
are constructed and studied in relation to the Fourier transform.
The contest between these transforms is informally commented on
in reference to signal processing, especially for video and image
compression. It is stated that wavelets are already competitive
with the Fourier transform for these applications, and head for the
identification of fingerprints. Samples of the developing theory
concerning these results are presented." }
%TTTT
@article{thomson.d:1977a,
Title = "Spectrum estimation techniques for characterization and
development of WT4 waveguide, I",
Author = "Thomson, David J.",
Journal = "Bell Syst. Tech. J.",
Volume = "56",
Year = "1977",
Pages = "1769--1815" }
@article{thomson.d:1977b,
Title = "Spectrum estimation techniques for characterization and
development of WT4 waveguide, II",
Author = "Thomson, David J.",
Journal = "Bell Syst. Tech. J.",
Volume = "56",
Year = "1977",
Pages = "1983--2005" }
@article{thomson.d:1982,
Author = "Thomson, David J.",
Title = "Spectrum estimation and harmonic analysis",
Journal = "Proc. IEEE",
Volume = "70",
Year = "1982",
Pages = "1055--1096",
Abstract = "In the choice of an estimator for the spectrum of a
stationary time series from a finite sample of the process, the
problems of bias control and consistency, or``smoothing'', are
dominant.
In this paper we present a new method based on a ``local''
eigenexpansion to estimate the spectrum in terms of the solution
of an integral equation. Computationally this method is
equivalent to using the weighted average of a series of
direct-spectrum estimates based on orthogonal data windows
(discrete prolate spheroidal sequences) to treat both the
bias and smoothing problems.
Some of the attractive features of this estimate are: there are
no {\it arbitrary} windows; it is a small sample theory; it is
consistent; it provides an analysis-of-variance test for line
components; and it has high resolution.
We also show relations of this estimate to maximum-likelihood
estimates, show that the {\it estimation capacity} of the
estimate is high, and show applications to coherence and
polyspectrum estimates." }
@article{thomson.d:1990a,
Author = "Thomson, David J.",
Title = "Time series analysis of Holocene climate data",
Journal = "Phil. Trans. R. Soc. Lond. A",
Volume = "330",
Year = "1990",
Pages = "601--616",
Abstract = "Holocene climate records are imperfect proxies for processes
containing complicated mixtures of periodic and random signals. I
summarize time series analysis methods for such data with emphasis on
the multiple-data-window technique. This method differs from
conventional approaches to time series analysis in that a set of
data tapers is applied to the data in the time domain before Fourier
transforming. The tapers, or data windows, are discrete prolate
spheroidal sequences characterized as being the most nearly
band-limited functions possible among functions defined on a finite
time domain. The multiple-window method is a small-sample theory
and essentially an inverse method applied to the finite Fourier
transform. For climate data it has the major advantage of providing
a narrowband F-test for the presence and significance of periodic
components and of being able to separate them from the non-deterministic
part of the process. Confidence intervals for the estimated quantities
are found by jackknifing across windows.
Applied to $^14$C records, this method confirms the presence of the
`Suess wiggles' and give an estimated period of 208.2 years. Analysis
of the thickness variations of bristlecone pine growth rings shows a
general absence of direct periodic components but a variation in the
structure of the time series with a 2360-year period." }
@article{thomson.d:1990b,
Author = "Thomson, David J.",
Title = "Quadratic-inverse spectrum estimates: applications to
palaeoclimatology",
Journal = "Phil. Trans. R. Soc. Lond. A",
Volume = "332",
Year = "1990",
Abstract = "This paper describes some new methods for the analysis
of time series and their application to find new results in
paleoclimate. The new statistical theory includes a quadratic
inverse theory for unbiased estimation of power spectra, an
associated test for spectral resolution, maximum-likelihood
spectrum estimates, and detailed explanations of some topics in
the detection and estimation of periodic components. A new
technique for estimating transfer functions is described. This
methodology is used to analyse series describing global ice volume
over the past 700,000 years as recorded by proxy oxygen isotope
ratios from deep-sea cores. We find many of the periodic components
predicted by the Milankovitch theory. However, systematic departures
are found from the predicated frequencies. These are accompanied
by phase modulation that can be attributed to changes in the
precession constant of the Earth caused by glaciation-induced
changes in the Earth's principal moments. An estimate of the
transfer function from ice volume to precession implies that the
Earth's crust requires more than 160,000 years to compensate for
mass redistribution, and overcompensates with a delay of about
24,000 years." }
@incollection{thomson.d-chave:1991,
Author = "Thomson, David J. and Alan D. Chave",
Title = "Jackknifed error estimates for spectra, coherences, and
transfer functions",
Booktitle = "Advances in Spectrum Analysis and Array Processing, Vol. 1",
Editor = "S. Haykin",
Publisher = "Prentice Hall",
Year = "1991",
Pages = "58--113" }
@article{thomson.d-lanzerotti-etal:1986,
Title = "Study of tidal periodicities using a transatlantic
telecommunications cable",
Author = "Thomson, David J. and L. J. Lanzerotti and L. V. Medford
and C. G. Maclennan and A. Meloni and G. P. Gregori",
Journal = "Geophys. Res. Lett.",
Volume = "13",
Year = "1986",
Pages = "525--528" }
@article{thomson.d-robbins-etal:1976,
Title = "Spectral and windowing techniques in power spectral
analysis of geomagnetic data",
Author = "Thomson, David J. and M. F. Robbins and C. G Maclennan and
L. J. Lanzerotti",
Journal = "Phys. Earth Planetary Interiors",
Volume = "12",
Year = "1976",
Pages = "217--231" }
%UUUU
%VVVV
@article{vautard-ghil:1989,
Author = "Vautard, R. and M. Ghil",
Title = "Singular spectrum analysis in nonlinear dynamics, with applications
to paleoclimatic time series",
Journal = "Physica D",
Volume = "35",
Year = "1989",
Pages = "395--424",
Abstract = "We distinguish between two dimensions of a dynamical system
given by experimental time series. {\it Statistical} dimension gives
a theoretical upper bound for the minimal number of degrees of freedom
required to describe the attractor up to the accuracy of the data,
taking into account sampling and noise problems. The {\it dynamical}
dimension is the intrinsic dimension of the attractor and does not
depend on the quality of the data.
Singular Spectrum Analysis (SSA) provides estimates of the statistical
dimension. SSA also describes the main physical phenomena reflected
by the data. It gives adaptive spectral filters associated with the
dominant oscillations of the system, and clarifies the noise
characteristics of the data.
We apply SSA to four paleoclimatic records. The principal climatic
oscillations, and the regime changes in their amplitude are
detected. About 10 degrees of freedom are statistically significant
in the data. Large noise and insufficient sample length do not allow
reliable estimates of the dynamical dimension." }
@article{vautard-yiou-etal:1992,
Author = "Vautard, Robert and Pascal Yiou and Michael Ghil",
Title = "Singular-spectrum analysis: A toolkit for short, noisy chaotic
signals",
Journal = "Physica D",
Volume = "58",
Year = "1992",
Pages = "95--126",
Abstract = "Singular Spectrum Analysis (SSA) is developed further, based
on experience with applications to geophysical timme series. It is
shown that SSA provides a crude but robust approximation of strange
attractors by tori, in the presence of noise. The method works
well for short, noisy time series.
The lagged-covariance matrix of the processes studied is the basis
of SSA. We select subsets of eigenelements and associated
principal components (PCs) in order to provide (i) a noise-reduction
algorithm, (ii) a detrending algorithm, and (iii) an algorithm for
the identification of oscillatory components. Reconstructed
components (RCs) are developed to provide optimal reconstruction
of a dynamic process at precise epochs, rather than averaged over
the window length of the analysis.
SSA is combined with advanced spectral-analysis methods--the
maximum entropy method (MEM) and the multi-taper method (MTM)--
to refine the interpretation of oscillatory behavior. A combined
SSA-MEM method is also used for the prediction of selected
subsets of RCs.
The entire toolkit is validated against a set of four prescribed
time series generated by known processes, quasi-periodic or
chaotic. It is also applied to a time series of global surface
temperatures, 130 years long, which has attracted considerable
attention in the context of the global warming issue and provides
a severe test for noise reduction and prediction." }
%WWWW
@article{walden.a:1990,
Author = "Walden, A. T.",
Title = "Improved low-frequency decay estimation using the
multitaper spectral analysis method",
Journal = "Geophysical Prospecting",
Volume = "38",
Year = "1990",
Pages = "61--86" }
@article{wilson.r-spann:1988,
Author = "Wilson, R. and M. Spann",
Title = "Finite prolate spheroidal sequences and their applications,
Pt. II",
Journal = "IEEE Trans. Patt. Anal. Mach. Intell.",
Volume = "PAMI-11",
Year = "1988",
Pages = "193--203" }
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[ home ]
Last updated or checked: Jan. 15, 1996
S. Baum
Dept. of Oceanography
Texas A&M University
baum@astra.tamu.edu