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Compact Trigonometric Fourier Series Exponential Fourier Series
"... • A periodic function f(t) can be represented by an infinite sum of sine and/or cosine functions that are harmonically related. That is, the frequency of any trigonometric term in the infinite series is an integral multiple, or harmonic, of the fundamental frequency of the periodic function. ..."
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• A periodic function f(t) can be represented by an infinite sum of sine and/or cosine functions that are harmonically related. That is, the frequency of any trigonometric term in the infinite series is an integral multiple, or harmonic, of the fundamental frequency of the periodic function.
Determining Lyapunov Exponents from a Time Series
 Physica
, 1985
"... We present the first algorithms that allow the estimation of nonnegative Lyapunov exponents from an experimental time series. Lyapunov exponents, which provide a qualitative and quantitative characterization of dynamical behavior, are related to the exponentially fast divergence or convergence of n ..."
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Cited by 495 (1 self)
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We present the first algorithms that allow the estimation of nonnegative Lyapunov exponents from an experimental time series. Lyapunov exponents, which provide a qualitative and quantitative characterization of dynamical behavior, are related to the exponentially fast divergence or convergence
A Practical Guide to Wavelet Analysis
, 1998
"... A practical stepbystep guide to wavelet analysis is given, with examples taken from time series of the El Nio Southern Oscillation (ENSO). The guide includes a comparison to the windowed Fourier transform, the choice of an appropriate wavelet basis function, edge effects due to finitelength t ..."
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Cited by 869 (3 self)
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A practical stepbystep guide to wavelet analysis is given, with examples taken from time series of the El Nio Southern Oscillation (ENSO). The guide includes a comparison to the windowed Fourier transform, the choice of an appropriate wavelet basis function, edge effects due to finite
Compressed sensing
, 2004
"... We study the notion of Compressed Sensing (CS) as put forward in [14] and related work [20, 3, 4]. The basic idea behind CS is that a signal or image, unknown but supposed to be compressible by a known transform, (eg. wavelet or Fourier), can be subjected to fewer measurements than the nominal numbe ..."
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Cited by 3625 (22 self)
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We study the notion of Compressed Sensing (CS) as put forward in [14] and related work [20, 3, 4]. The basic idea behind CS is that a signal or image, unknown but supposed to be compressible by a known transform, (eg. wavelet or Fourier), can be subjected to fewer measurements than the nominal
Locally Adaptive Dimensionality Reduction for Indexing Large Time Series Databases
 In proceedings of ACM SIGMOD Conference on Management of Data
, 2002
"... Similarity search in large time series databases has attracted much research interest recently. It is a difficult problem because of the typically high dimensionality of the data.. The most promising solutions' involve performing dimensionality reduction on the data, then indexing the reduced d ..."
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Cited by 316 (33 self)
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Similarity search in large time series databases has attracted much research interest recently. It is a difficult problem because of the typically high dimensionality of the data.. The most promising solutions' involve performing dimensionality reduction on the data, then indexing the reduced
Differentialdifference equations
, 1963
"... are solved, where either f(x) or g(x) is specified in certain intervals in the range 0 ^ x < oo, with up to four intervals. r(f) may be different for different intervals. It is shown that the solution is closely allied to that of a type of FourierBessel series with mixed boundary values so that ..."
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Cited by 331 (0 self)
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are solved, where either f(x) or g(x) is specified in certain intervals in the range 0 ^ x < oo, with up to four intervals. r(f) may be different for different intervals. It is shown that the solution is closely allied to that of a type of FourierBessel series with mixed boundary values so
Efficient time series matching by wavelets
 Proc. of 15th Int'l Conf. on Data Engineering
, 1999
"... Time series stored as feature vectors can be indexed by multidimensional index trees like RTrees for fast retrieval. Due to the dimensionality curse problem, transformations are applied to time series to reduce the number of dimensions of the feature vectors. Different transformations like Discrete ..."
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Cited by 286 (1 self)
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Time series stored as feature vectors can be indexed by multidimensional index trees like RTrees for fast retrieval. Due to the dimensionality curse problem, transformations are applied to time series to reduce the number of dimensions of the feature vectors. Different transformations like
The FourierSeries Method For Inverting Transforms Of Probability Distributions
, 1991
"... This paper reviews the Fourierseries method for calculating cumulative distribution functions (cdf's) and probability mass functions (pmf's) by numerically inverting characteristic functions, Laplace transforms and generating functions. Some variants of the Fourierseries method are remar ..."
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Cited by 211 (52 self)
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This paper reviews the Fourierseries method for calculating cumulative distribution functions (cdf's) and probability mass functions (pmf's) by numerically inverting characteristic functions, Laplace transforms and generating functions. Some variants of the Fourierseries method
Bucket Elimination: A Unifying Framework for Reasoning
"... Bucket elimination is an algorithmic framework that generalizes dynamic programming to accommodate many problemsolving and reasoning tasks. Algorithms such as directionalresolution for propositional satisfiability, adaptiveconsistency for constraint satisfaction, Fourier and Gaussian elimination ..."
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Cited by 298 (58 self)
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Bucket elimination is an algorithmic framework that generalizes dynamic programming to accommodate many problemsolving and reasoning tasks. Algorithms such as directionalresolution for propositional satisfiability, adaptiveconsistency for constraint satisfaction, Fourier and Gaussian
EXPONENTIAL APPROXIMATIONS USING FOURIER SERIES PARTIAL SUMS
, 1997
"... The problem of accurately reconstructing a piecewise smooth, 2πperiodic function f and its first few derivatives, given only a truncated Fourier series representation of f, is studied and solved. The reconstruction process is divided into two steps. In the first step, the first 2N + 1 Fourier coef ..."
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Cited by 7 (0 self)
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The problem of accurately reconstructing a piecewise smooth, 2πperiodic function f and its first few derivatives, given only a truncated Fourier series representation of f, is studied and solved. The reconstruction process is divided into two steps. In the first step, the first 2N + 1 Fourier
Results 1  10
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