Topic: Communication Systems
If x and y are two random signals with zero mean Gaussian distribution having identical standard deviation, the phase angle between them is
- A. zero mean Gaussian distributed
- B. uniform between -$\pi$ and $\pi$
- C. uniform between -$\pi/2$ and $\pi/2$
- D. non-zero mean Gaussian distributed
Answer: B. uniform between -$\pi$ and $\pi$
Explanation: When x and y are two independent zero-mean Gaussian random variables with identical standard deviations, they form a circularly symmetric complex Gaussian random variable. In polar coordinates, the phase angle $\theta = \tan^{-1}\left(\frac{y}{x}\right)$ of such a distribution is uniformly distributed between $-\pi$ to $\pi$.