The covariance function, C_x(τ), of a stationary stochastic process, x(t), is said to be positive definite. This means that

A) $${C_x}\left( \tau \right) \geqslant 0{\text{ for all }}\tau $$ B) $$\int\limits_{ - \infty }^\infty {{C_x}\left( \tau \right)d\tau \geqslant 0} $$ C) $$\int\limits_{ - \infty }^\infty {{C_x}\left( \tau \right)\exp \left( { - j\omega \tau } \right)d\tau \geqslant 0} {\text{ }}$$ D) $${C_x}\left( 0 \right) \geqslant 0$$

Answer & Solution

Correct Answer: Option A

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The covariance function Cx( ) of a stationary stochastic process x(t)...

The covariance function, Cx(τ), of a stationary stochastic process, x(t), is said to be positive definite. This means that

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The covariance function, C_x(τ), of a stationary stochastic process, x(t), is said to be positive definite. This means that