Question

Consider the random process x(t) = a cos(wt) where w is a constant and a is a random variable uniformly distributed.

A) Gaussian Process
B) White Noise Process
C) Random Signal Process
D) Sinusoidal Process

Answer 1

The random process x(t) = a cos(wt) is a Sinusoidal Process with a uniform distribution for the amplitude a.

Step-by-step explanation:

The random process x(t) = a cos(wt) is known as a Sinusoidal Process. This process involves a cosine wave with a frequency w, and the amplitude a is a random variable that is uniformly distributed.

a. The random variable X is the amplitude a of the cosine wave.

b. X~ represents that X is a random variable.

c. The probability distribution of X, which represents the amplitude a, would be a uniform distribution.

d. The distribution of the random variable X, which represents the amplitude a, is uniform.