Generate numerically a white gaussian random process and

Question

1. Delay Spread

There are two rays with arrival times at 10msec and 11m sec. Find the power weighted mean arrival time and power weighted delay spread (i.e., rms delay spread) for the following two cases:

a) Power of ray 1 is equal to power of ray 2.

b) Power of ray 1 is 9 times of power of ray 2.

Problem-2 Linear System

Part I

Generate numerically a white Gaussian random process and demonstrate numerically its autocorrelation function is a delta function and its power spectrum is white, i.e., flat.

Part II

Consider a linear system with impulse response h(t). Let the stationary random process x(t) be its input and the stationary random process y(t) be its output.  Let a_x(t) be the autocorrelation of x(t) and a_y(t) be the autocorrelation of y(t). Prove analytically that  a_y(t)=a_x(t)xh(t)xh(-t) and its Fourier transformed equivalent A₁(ω) = A_x(ω) |H(ω)|

Part III

Consider the impulse response h(t)=1-0.01*t   for   1<=t <=100   and h(t)=0 elsewhere. Let the input x(t) is a white Gaussian random process. Generate the output y(t) and prove that  a_y(t)= h(t)xh(-t) numerically.

Attachment:- Assignment-96023.doc