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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 ax(t) be the autocorrelation of x(t) and ay(t) be the autocorrelation of y(t). Prove analytically that ay(t)=ax(t)xh(t)xh(-t) and its Fourier transformed equivalent A1(ω) = Ax(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 ay(t)= h(t)xh(-t) numerically.
Attachment:- Assignment-96023.doc
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