Alias-free randomly timed sampling of stochastic processes

Beutler, Frederick J.

doi:10.1109/tit.1970.1054435

Cited by 106 publications

(51 citation statements)

References 9 publications

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“…A third class of processes X is the 'jittered' grid of Akaike (1960), Beutler (1970 and Reimann (1994), where X j = j + U j , j ≥ 1, and the variables U j are independent and Uniformly distributed on (− 1 2 , 1 2 ). Call this model (M X,3 ).…”

Section: Models and Methodologymentioning

confidence: 99%

Nonparametric estimation of a periodic function

Hall¹,

Reimann²,

Rice³

2000

Biometrika

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ABSTRACT. Motivated by applications to brightness data on periodic variable stars, we study nonparametric methods for estimating both the period and the amplitude function from noisy observations of a periodic function made at irregularly spaced times. It is shown that nonparametric estimators of period converge at parametric rates and attain a semiparametric lower bound which is the same if the shape of the periodic function is unknown as if it were known. Also, first-order properties of nonparametric estimators of the amplitude function are identical to those that would obtain if the period were known. Numerical simulations and applications to real data show the method to work well in practice.KEY WORDS AND PHRASES. frequency estimation, nonparametric regression, semiparametric estimation, Nadaraya-Watson estimator, MACHO project, variable star data.

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Section: Models and Methodologymentioning

confidence: 99%

Nonparametric estimation of a periodic function

Hall¹,

Reimann²,

Rice³

2000

Biometrika

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“…Later in the 1970s, Beutler [8] generalized the formulation of the alias-free sampling problem and studied special cases depending on the spectral distribution of the signals. In this context, Masry [9] studied the random sampling in a more general framework.…”

Section: Beyond Nyquist Sampling Ratementioning

confidence: 99%

Sparse correlation matching-based spectrum sensing for open spectrum communications

Lagunas

Nájar

2012

EURASIP J. Adv. Signal Process.

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To deal with the current spectrum scarcity problem and exploiting the fact that exclusive access through tightly regulated licensing leads to idle spectrum, cognitive radio has been proposed as a way to reuse this underutilized spectrum in an opportunistic manner, i.e., allowing the use of temporarily unused licensed spectrum to secondary users who have no spectrum licenses. To protect the licensed users from the cognitive users' interference, the opportunistic user requires knowledge of the original license holder activity. In this article, a feature-based approach for spectrum sensing based on periodic non-uniform sampling is addressed. In particular, we face the compressed-sampling version of detecting predetermined spectral shapes in sparse wideband regimes by means of a correlation-matching procedure.

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“…The key properties of Poisson sampling, which is the basis for our work, were derived in the 1970s [7], [8], and are nicely summarized in [9]. We adapt these concepts to network measurement using Poisson counter-driven stochastic differential equations (PCDSDE) models.…”

Section: Related Workmentioning

confidence: 99%

“…In a sense, it can be viewed as a stochastic approximation to uniform sampling since it can be shown that Poisson samples over any finite interval have a uniform distribution [7], [8]. In particular, using the properties of Poisson point processes it is shown in [9] that if a deterministic signal f (t) has Fourier transform F (ω), an unbiased estimate of F (ω) can be obtained in the form…”

Section: A Theoretical Foundations Of Random Samplingmentioning

confidence: 99%

Stochastic Sampling for Internet Traffic Measurement

Wolf

Cai

Kelly

et al. 2007

2007 IEEE Global Internet Symposium

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Abstract-The increasing complexity of the Internet demands continued improvements to measurement techniques and data analysis methods to aid our understanding of network operation. The availability of accurate measurement data is necessary in many areas ranging from attack detection, novel pricing schemes, buffer dimensioning and switch design to general network management. In this paper, we develop a theory for accurate and unbiased Internet traffic measurement using the tools of Poisson random sampling. We show how this approach helps in storing, managing, and aggregating data from different sources with independent clocks and sampling rates. We present results that show that stochastic sampling maintains important information about network measurements that would be lost when using conventional uniform sampling.

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Alias-free randomly timed sampling of stochastic processes

Cited by 106 publications

References 9 publications

Nonparametric estimation of a periodic function

Nonparametric estimation of a periodic function

Sparse correlation matching-based spectrum sensing for open spectrum communications

Stochastic Sampling for Internet Traffic Measurement

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