On the Fourier Expansion of Stationary Random Processes
نویسنده
چکیده
The purpose of this note is to demonstrate that in the Fourier expansion of a quasistationary random continuous process with continuous covariance function, the amplitudes of the frequency components do not possess the desirable property of being mutually uncorrelated unless the process degenerates to a single random variable in its range of definition. Specifically we consider a real-valued continuous random process x(t) observed during a time interval T. We assume that the mean and covariance function of x(t) exist, so with no loss in generality we assume that
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