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17
Fast Fourier transforms for nonequispaced data: A tutorial
, 2000
"... In this section, we consider approximative methods for the fast computation of multivariate discrete Fourier transforms for nonequispaced data (NDFT) in the time domain and in the frequency domain. In particular, we are interested in the approximation error as function of the arithmetic complexity o ..."
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Cited by 111 (33 self)
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In this section, we consider approximative methods for the fast computation of multivariate discrete Fourier transforms for nonequispaced data (NDFT) in the time domain and in the frequency domain. In particular, we are interested in the approximation error as function of the arithmetic complexity of the algorithm. We discuss the robustness of NDFTalgorithms with respect to roundoff errors and apply NDFTalgorithms for the fast computation of Bessel transforms.
Nonuniform Fast Fourier Transforms Using MinMax Interpolation
 IEEE Trans. Signal Process
, 2003
"... The FFT is used widely in signal processing for efficient computation of the Fourier transform (FT) of finitelength signals over a set of uniformlyspaced frequency locations. However, in many applications, one requires nonuniform sampling in the frequency domain, i.e.,a nonuniform FT . Several pap ..."
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Cited by 83 (13 self)
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The FFT is used widely in signal processing for efficient computation of the Fourier transform (FT) of finitelength signals over a set of uniformlyspaced frequency locations. However, in many applications, one requires nonuniform sampling in the frequency domain, i.e.,a nonuniform FT . Several papers have described fast approximations for the nonuniform FT based on interpolating an oversampled FFT. This paper presents an interpolation method for the nonuniform FT that is optimal in the minmax sense of minimizing the worstcase approximation error over all signals of unit norm. The proposed method easily generalizes to multidimensional signals. Numerical results show that the minmax approach provides substantially lower approximation errors than conventional interpolation methods. The minmax criterion is also useful for optimizing the parameters of interpolation kernels such as the KaiserBessel function.
Efficient Algorithms for DiffusionGenerated Motion by Mean Curvature
 J. Comput. Phys
, 1996
"... We accept this thesis as conforming to the required standard ..."
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Cited by 21 (5 self)
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We accept this thesis as conforming to the required standard
Statistical Significance of periodicity and logperiodicity with heavytailed correlated Noise
, 2001
"... We estimate the probability that random noise, of several plausible standard distributions, creates a false alarm that a periodicity (or logperiodicity) is found in a time series. The solution of this problem is already known for independent Gaussian distributed noise. We investigate more general s ..."
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Cited by 12 (7 self)
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We estimate the probability that random noise, of several plausible standard distributions, creates a false alarm that a periodicity (or logperiodicity) is found in a time series. The solution of this problem is already known for independent Gaussian distributed noise. We investigate more general situations with nonGaussian correlated noises and present synthetic tests on the detectability and statistical significance of periodic components. A periodic component of a time series is usually detected by some sort of Fourier analysis. Here, we use the Lomb periodogram analysis which is suitable and outperforms Fourier transforms for unevenly sampled time series. We examine the falsealarm probability of the largest spectral peak of the Lomb periodogram in the presence of powerlaw distributed noises, of shortrange and of longrange fractionalGaussian noises. Increasing heavytailness (respectively correlations describing persistence) tends to decrease (respectively increase) the falsealarm probability of finding a large spurious Lomb peak. Increasing antipersistence tends to decrease the falsealarm probability. We also study the interplay between heavytailness and longrange correlations. In order to fully determine if a Lomb peak signals a genuine rather than a spurious periodicity, one should
A Comparison of Poisson and Uniform Sampling for Active Measurements
"... Active probes of network performance represent samples of the underlying performance of a system. Some effort has gone into considering appropriate sampling patterns for such probes: i.e. there has been significant discussion of the importance of sampling using a Poisson process to avoid biases intr ..."
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Cited by 7 (0 self)
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Active probes of network performance represent samples of the underlying performance of a system. Some effort has gone into considering appropriate sampling patterns for such probes: i.e. there has been significant discussion of the importance of sampling using a Poisson process to avoid biases introduced by synchronization of system and uniformly spaced probes. However, there are unanswered questions about whether Poisson probing has costs in terms of sampling efficiency, and there is some misinformation about what types of inferences are possible based on different probe patterns. This paper provides a quantitative comparison of different sampling methods, both in terms of efficiency. The paper also shows that the irregularity in probing patterns is useful not just in avoiding synchronization, but also in determining frequency domain properties of a system. The paper provides a firm basis for practitioners or researchers to use in making such a decision about the type of sampling they should use in a particular application, along with methods for the analysis of their outputs.
2005: Statistical characterization of zonal and meridional ocean wind stress
 J. Atmos. Oceanic Technol
"... Four years of ocean vector wind data are used to evaluate statistics of wind stress over the ocean. Raw swath wind stresses derived from the Quick Scatterometer (QuikSCAT) are compared with five different global gridded wind products, including products based on scatterometer observations, meteorolo ..."
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Cited by 5 (4 self)
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Four years of ocean vector wind data are used to evaluate statistics of wind stress over the ocean. Raw swath wind stresses derived from the Quick Scatterometer (QuikSCAT) are compared with five different global gridded wind products, including products based on scatterometer observations, meteorological analysis winds from the European Centre for MediumRange Weather Forecasts, and reanalysis winds from the National Centers for Environmental Prediction. Buoy winds from a limited number of sites in the Pacific Ocean are also considered. Probability density functions (PDFs) computed for latitudinal bands show that mean wind stresses for the six global products are largely in agreement, while variances differ substantially, by a factor of 2 or more, with swath wind stresses indicating highest variances for meridional winds and for zonal winds outside the Tropics. Higher moments of the PDFs also differ. Kurtoses are large for all wind products, implying that PDFs are not Gaussian. None of the available gridded products fully captures the range of extreme wind events seen in the raw swath data. Frequency spectra for the five gridded products agree with frequency spectra from swath data at low frequencies, but spectral slopes differ at higher frequencies, particularly for frequencies greater than 100
Frequency Estimation Using UnequallySpaced Astronomical Data
, 1994
"... This thesis studies estimation of the frequency of a periodic function of time, when the function is observed with noise at a collection of unequallyspaced times. This research was motivated by the detection and classification of variable stars in astronomy. Most of the statistical literature on f ..."
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Cited by 3 (1 self)
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This thesis studies estimation of the frequency of a periodic function of time, when the function is observed with noise at a collection of unequallyspaced times. This research was motivated by the detection and classification of variable stars in astronomy. Most of the statistical literature on frequency estimation assumes equallyspaced times, but observation times in astronomy are often unequallyspaced with a sampling distribution that contains periodic effects due to being able to collect data only at certain times of day. In Chapter 1 we describe the database of variable stars collected by the MACHO collaboration and present examples which illustrate the common types of variable stars and the nature of the estimation problem. In Chapter 2 we provide background material and give models for the periodic function and sampling times. We derive the ...
Searching for Periodic Gene Expression Patterns Using
"... The LombScargle periodogram approach was applied to the search for periodically expressed genes in a Plasmodium falciparum dataset. The LombScargle algorithm has several computational advantages over more common approaches, such as Fourier analysis, including direct treatment of missing values and ..."
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The LombScargle periodogram approach was applied to the search for periodically expressed genes in a Plasmodium falciparum dataset. The LombScargle algorithm has several computational advantages over more common approaches, such as Fourier analysis, including direct treatment of missing values and and a periodogram that has known statistical properties. Hierarchical clustering of periodograms shows explicit partitioning of multiple periodicities present in some gene expression patterns. The LombScargle algorithm performance was compared to earlier analysis of CAMDA 2004 challenge dataset by Bozdech et al. [1], based on Fast Fourier Transforms (FFT). We identified an additional 265 genes with 48hr periodic expression, which were not considered by the FFT because they had too many missing values. We also automatically detected, in the same analysis, expression patterns with periodicity close to 24 hr, and other interesting patterns. Keywords LombScargle periodogram, periodicity, gene expression profile,
K.Suresh Reddy, S.Venkata Chalam & B.C.Jinaga A New Enhanced Method of Non Parametric power spectrum Estimation.
"... The spectral analysis of non uniform sampled data sequences using Fourier Periodogram method is the classical approach.In view of data fitting and computational standpoints why the Least squares periodogram (LSP) method is preferable than the “classical ” Fourier periodogram and as well as to the fr ..."
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The spectral analysis of non uniform sampled data sequences using Fourier Periodogram method is the classical approach.In view of data fitting and computational standpoints why the Least squares periodogram (LSP) method is preferable than the “classical ” Fourier periodogram and as well as to the frequentlyused form of LSP due to Lomb and Scargle is explained. Then a new method of spectral analysis of nonuniform data sequences can be interpreted as an iteratively weighted LSP that makes use of a datadependent weighting matrix built from the most recent spectral estimate. It is iterative and it makes use of an adaptive (i.e., datadependent) weighting, we refer to it as the iterative adaptive approach (IAA).LSP and IAA are nonparametric methods that can be used for the spectral analysis of general data sequences with both continuous and discrete spectra. However, they are most suitable for data sequences with discrete spectra (i.e., sinusoidal data), which is the case we emphasize in this paper. Of the existing methods for nonuniform sinusoidal data, Welch, MUSIC and ESPRIT methods appear to be the closest in spirit to the IAA proposed here. Indeed, all these methods make use of the estimated covariance matrix that is computed in the first iteration of IAA from LSP. Comparative study of LSP with MUSIC and ESPRIT methods are discussed.