On the reconstruction error of sampled data estimates (Corresp.)

Ephremides, Anthony; Brandenburg, L.

doi:10.1109/tit.1973.1055010

Cited by 5 publications

(2 citation statements)

References 6 publications

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“…This result shows that some care must be exercised in studying continuoustime problems via discretization. Some studies of this question have recently been made [318]. Some other special examples of processes of multiplicity one (e.g., wide-sense Markov processes and certain harmonizable processes) have been given by Cramer [275], [300], who was apparently unaware of the class of processes identified by Levy [cf.…”

Section: Processes Of Multiplicity Onementioning

confidence: 99%

A view of three decades of linear filtering theory

Kailath

1974

IEEE Trans. Inform. Theory

612

164

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Section: Processes Of Multiplicity Onementioning

confidence: 99%

A view of three decades of linear filtering theory

Kailath

1974

IEEE Trans. Inform. Theory

612

164

View full text Add to dashboard Cite

“…No bounds are available on the loss of information entailed by examining a continuous-time random process at only discrete instants of time. 22 Two critical remarks concerning the method of recording the data should be made : first, there are no quantitative measures available on the amount of noise introduced into the data by the measurement system alone. Presumably, any measurement system noise was in significant compared to the telephone channel noise.…”

Section: Description Of the Datamentioning

confidence: 99%

A Statistical Analysis of Telephone Noise

Stuck¹,

Kleiner²

1974

Bell System Technical Journal

122

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The results of a statistical analysis of telephone noise are presented. The analysis consists of two stages: an exploratory data analysis stage, where the data are characterized through various nonparametric statistics and a model‐building stage, where the data are matched to models. The exploratory data analysis stage involved examination of noise waveforms, power spectra, and covariance estimates. The results show that telephone noise consists of a deterministic component (sinusoids at various frequencies) and a stochastic component. It is assumed that these components add. The data are filtered to remove the deterministic component. Next, central moment estimates are presented, as well as first‐order amplitude statistics (histograms and empirical cumulative distributions) for these filtered data. The results indicate that the filtered data appear wide‐sense stationary over short periods of time (typically 1 second) and, although close to gaussian, are distinctly nongaussian. The model‐building stage involved fitting the filtered data to two classes of models. The first class of models is based on symmetric stable distributions that arise from the central limit theorem. The second class of models assumes two different physical processes that contribute to the random component of telephone noise: The low‐variance process is assumed to be gaussian, while the high‐variance component is assumed to be a filtered Poisson process. Both classes of models agree intuitively with the physical processes generating telephone noise and are mathematically tractable. Based largely on graphical tests, both models appear to fit the filtered data reasonably well.

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A property of random processes with unit multiplicity

Ephremides

1977

Journal of Multivariate Analysis

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On the reconstruction error of sampled data estimates (Corresp.)

Cited by 5 publications

References 6 publications

A view of three decades of linear filtering theory

A view of three decades of linear filtering theory

A Statistical Analysis of Telephone Noise

A property of random processes with unit multiplicity

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