3) When did you start your simulations: Consider the simulation of a first order auto- regressive, or AR(1), process. A wide-sense stationary real white noise process x[n] with autocorrelation Rxx[m] =56[m] is passed through the AR(1) filter with a = 0.5, such that the output is y[n] = x[n] +0.5y[n-1]. x[n] H(z)=; 1 1-0.52-1 y[n] 3.1) (3.1.a) Assume the above filter operates at all times. Then y[n] is jointly wide-sense stationary. Find the cross-correlation between x[n] and y[n], Rxy[m] = E(x[nly[n]}, where m n-n2. [Hint: There are many ways to solve this problem. You may use the frequency domain or the z domain approach, finding Sxy (w) or Sxy (2) first, and then taking the inverse Fourier or transform. You may express y[n] as a convolution of x[n] with h[n] (impulse response), multiply the equation by x[n], and take the expectation.] Rxy[m] = (3.1.b) Find the autocorrelation of the AR(1) process, Ryy[m]. Ryy[m] = for m> 0 for m0 (4 marks) (2 marks)