PROBLEM 2(20%) Consider a DT LTI system, H2 with a unit sample response h2(n=hn] *h(n+l], as shown below, where hn=8n-8n-1. You may remember from one of the lectures that h(] 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 h 一[一 d(n 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 p[n=an] Provide a labeled sketch of yn, the output of the system 2 plnPROBLEM 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 y[n] n −7 −6 −5 −4 −3 −2 −1 1 2 3 4 5 6 7 4