Show by example that the random process Z (t) = X (t) + Y (t) may be a wide sense stationary process even though the random processes X (t) and Y (t) are not.Let and be independent, wide sense stationary random processes with zero- means and identical autocorrelation functions. Then let X (t) = A (t) sin (t) Y (t) = B (t) cos (t) and Show that X (t) and Y (t) are not wide sense stationary. Then show that Z (t) is wide sense stationary.
Answer to relevant QuestionsLet X (t) = A(t) cos (ω0t + θ), where A(t) is a wide sense stationary random process independent of θ and let θ be a random variable distributed uniformly over . Define a related process Y (t) = A (t) cos((ω0 +ω1) t + ...A random process is defined by X (t) = exp (– At) u (t) where A is a random variable with PDF, fA (a). (a) Find the PDF of X (t) in terms of fA (a). (b) If is an exponential random variable, with fA (a) = e– au (a), ...A stationary random process, X (t), has a mean of μX and correlation function, RX, X (t). A new process is formed according to Y (t) = aX (t) + b for constants and. Find the correlation function in terms of μX and R X,X ...Consider a Poisson counting process with arrival rate λ. (a) Suppose it is observed that there is exactly one arrival in the time interval [0, to]. Find the PDF of that arrival time. (b) Now suppose there were exactly two ...Model lightning strikes to a power line during a thunderstorm as a Poisson impulse process. Suppose the number of lightning strikes in time interval t has a mean rate of arrival given by s, which is one strike per 3 minutes. ...
Post your question