PROBLEM 2 (20%0) Consider a DT LTI system, H2 with a unit sample response h2/n= hn *hn+l], as shown below, where hn]=8n-8n-1. You may remember from one of the lectures that h(n can be viewed as the unit sample response of a DT lti system that acts as an edge detector The purpose of this problem is to develop an edge detector that is robust against additive noise h2[nl System H2 h2n dnI Part a. Assume that the input to the system, pIn] is as shown below, and there is no noise, i.e., d(n=0 and pIn]= n. Provide a labeled sketch of yIn, the output of the system 3-2-101 yn−2 1 PROBLEM 2 (20%) Consider a DT LTI system, H2 with a unit sample response h2[n] = h[n]↔h[n+1], as shown below, where h[n] = �[n] − �[n − 1]. You may remember from one of the lectures that h[n] can be viewed as the unit sample response of a DT LTI system that acts as an edge detector. The purpose of this problem is to develop an edge detector that is robust against additive noise. h2[n] 1 1 System H2 x[n] + 0 p[n] h2[n] y[n] n −2 −1 1 2 d[n] −2 Part a. Assume that the input to the system, p[n] is as shown below, and there is no noise, i.e., d[n] = 0 and p[n] = x[n]. Provide a labeled sketch of y[n], the output of the system. 2 2 2 2 p[n] −4 −3 −2 −1 0 1 2 3 n −7 −6 −5 −4 −3 −1 2 3 4 5 6 7 y[n] n 2 −2 −2 2 4