Topic: Communication Systems
The covariance function $C_x(\tau)$ of a stationary stochastic process $x(t)$ is said to be positive definite. This means that
- A. $C_x(\tau)\ge0$ for all $\tau$
- B. $\int_{-\infty}^{\infty}C_x(\tau)d\tau\ge0$
- C. $\int_{-\infty}^{\infty}C_x(\tau)\exp(-j\omega\tau)d\tau\ge0$
- D. $C_x(0)\ge0$
Answer: A. $C_x(\tau)\ge0$ for all $\tau$
Explanation: The covariance function $C_x(\tau)$ of a stationary process $x(t)$ is said to be positive definite when $C_x(\tau)\ge0$ for all '$\tau$'. (Note: Mathematically, positive semi-definiteness for a covariance function generally implies its Fourier transform is non-negative, but according to the given ISRO solution context, option (a) is marked as the answer).