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The covariance function $$C_x (\tau)$$ of a stationary stochastic process x(t) is said to be positive definite. This means that
$$C_x(\tau) \geq 0 for all \tau$$
$$\int_{-\infty}^{\infty}C_x(\tau) d\tau \geq 0 $$
$$\int_{-\infty}^{\infty}C_x(\tau) exp(-j \omega \tau) d \tau \geq 0 $$
$$C_x(0) \geq 0 $$
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