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Locally stationary random processes

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1 Author(s)

A new kind of random process, the locally stationary random process, is defined, which includes the stationary random process as a special case. Numerous examples of locally stationary random processes are exhibited. By the generalized spectral density \Psi (\omega , \omega \prime ) of a random process is meant the two-dimensional Fourier transform of the covariance of the process; as is well known, in the case of stationary processes, \Psi (\omega , \omega \prime ) reduces to a positive mass distribution on the line \omega = \omega \prime in the \omega , \omega \prime plane, a fact which is the gist of the familiar Wiener-Khintchine relations. In the case of locally stationary random processes, a relation is found between the covariance and the spectral density which constitutes a natural generalization of the Wiener-Khintchine relations.

Published in:

IRE Transactions on Information Theory  (Volume:3 ,  Issue: 3 )