Question 2 (30 points) Zero mean white noise, w), wtower spectral density of e w

Question

Question 2 (30 points) Zero mean white noise, w), wtower spectral density of e will be passed through a lincar filter. The filter is given by: h(t) = 2000)sinc(2000(t-0.05)Ju(t) Determine the following (use MATLAB for all plots): (a) Determine the frequency response of the filter analytically. What type of filter does h(1) represent? Can the output of the filter, n(), be determined using convolution when the input is w(t)? Explain your answer (b) Determine the power spectral density of the output process, n) (c) Determine the auto-correlation function of the output process, n(t) (d) Find the mean and variance of the output process, n(t) (e) Determine the AC and DC power components of the output process, n(t)

Explanation / Answer

a) The FT of h(t) is rectangular pulse so h(t) represents low pass filter.

Given filter is linear so we can apply convolution. The PSD of output=(FT of h(t) )2 *PSD of input

b)The PSD of output=(FT of h(t) )2 *PSD of input

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