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Consider the Gaussian function

1508_Equation 2.jpg

which is Fourier transformable. Moreover, it is an even function of t, thereby satisfying the symmetry property of the autocorrelation function around the origin t = 0.

Apply the Wiener- Khintchine theorem to confirm that ƒ(t)is indeed a legitimate normalized autocorrelation function of a weakly stationary process.

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