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Abstract

1See Anderson (1971), Sec. 5.7.1, where it is proved that if B(τ) = 0 for |τ| > n, then numbers b0, b1, …, bn can be found which satisfy (2.5). Let us now consider the more general case of the complex-valued function B(τ). Assuming that bk = 0 for k > n and k < 0, we can write the corresponding generalization of the result (2.5) in the form
$$B(t - s) = \sum\limits_{k = ^{ - \infty } }^\infty {b_{k + t - 8} } \bar b_k = \sum\limits_{j = ^{ - \infty } }^\infty {b_{t - j} \bar b_{8 - j} }$$
(2.1)
. The last relationship implies the possibility of representing the random sequence X(t) in the form (2.4) by virtue of the so-called theorem on generalized spectral representation of random functions (see the closing part of Note 17 below).

Keywords

Correlation Function Spectral Density Random Function Stationary Sequence Discontinuity Point 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag New York Inc. 1987

Authors and Affiliations

  • A. M. Yaglom
    • 1
  1. 1.Institute of Atmospheric PhysicsAcademy of Sciences of the U.S.S.R.MoscowUSSR

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