Frequency Responses

The questions below are due on Thursday April 10, 2025; 02:00:00 PM.

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Part 1

Determine X(\Omega), the DTFT of x[n], where

x[n] = \sum_{k=0}^\infty a^k\delta[n-5k] = \delta[n] + a\delta[n-5] + a^2\delta[n-10] + \ldots

Enter a closed-form expression for X(\Omega) in the box below (use OMEGA for \Omega):

X(\Omega) =~

Part 2

Find the frequency response H_1(\Omega) of a linear, time-invariant system whose unit-sample response h_1[n] is shown below (h_1[n] is zero outside the indicated range):

Enter a closed-form expression for the frequency response in the box below (use OMEGA for \Omega).

H_1(\Omega) =~

Part 3

Find the frequency response H_2(\Omega) of a linear, time-invariant system whose unit-sample response h_2[n] is shown below:

Enter a closed-form expression for the frequency response in the box below (use OMEGA for \Omega).

H_2(\Omega) =~