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Book Chapter

Sampling

Published:
January 01, 2008

Abstract

Discrete-time signals are sequences of numbers, with each number being identified by a fixed time instant. Such a series of data in a time sequence is called a time series. In other words, a time series xn is a series of data, with each data value xn being associated with a discrete, equally spaced time index n. The time index n is taken to be a whole number, or integer.

Time series occur in all branches of science (Wold, 1938; Kolmogorov, 1941; Wiener, 1942). Economic data always appear in the form of numerical time series. Some meteorologic data, such as daily temperatures, are numerical time series; other meteorologic data, such as continuous barographic records, are continuous-time signals. Continuous-time signals appear in the engineering, biological, and physical sciences. Such continuous-time signals can be read (or measured, observed, or sampled) at equal intervals of time, thereby generating time series (Robinson and Silvia, 1979, 1980).

Because a time series represents only the sampled values of a continuous-time signal, it provides only a limited description of the signal. By taking the sampling instants close enough together, the amount of information that is lost by replacing a well-behaved continuous-time function by a time series can be made small. A time spacing that is too gross would mean substantial information loss in the sampling process. At the other extreme, a time spacing that is too fine would mean substantial redundancy in information produced by the sampling

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Contents

Society of Exploration Geophysicists Geophysical References Series

Digital Imaging and Deconvolution: The ABCs of Seismic Exploration and Processing

Enders A. Robinson
Enders A. Robinson
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Sven Treitel
Sven Treitel
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Society of Exploration Geophysicists
Volume
15
ISBN electronic:
9781560801610
Publication date:
January 01, 2008

GeoRef

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