Part b. For the same input signal as Part a, now assume that the noise signal is d{n]=-6n+1 Provide a labeled sketch of the output y/n, i.e., the response to n]=pn +dn
−2 1 Part b. For the same input signal as Part a., now assume that the noise signal is d[n] = −�[n + 1]. Provide a labeled sketch of the output y[n], i.e., the response to x[n] = p[n] + d[n]. −7 −6 −5 −4 −3 −1 2 3 4 5 6 7 y[n] n 2 2 −1 −2 2 −3 6
Fall 2003: Quiz 1 NAME: Work Page for Problem 2 y[n]=an* ha[n (p{n+d{m])*h2l] (Pn*h2回])+(dn]*h2]) We have already found (p[n]* h2(n) in Part a. Now we need d(n]* h2n d(n]* hsIn Adding the above(dn]* h2[nd) to the answer in Part a, we get y[n for this part which is shown on page 6 7 Problem 2 continues on the following page
−1 −2 0 Fall 2003: Quiz 1 NAME: Work Page for Problem 2 y[n] = x[n] ↔ h2[n] = (p[n] + d[n]) ↔ h2[n] = (p[n] ↔ h2[n]) + (d[n] ↔ h2[n]) We have already found (p[n] ↔ h2[n]) in Part a. Now we need d[n] ↔ h2[n]. d[n] −2 0 1 n −1 −1 1 n d[n] ↔ hs[n] −1 2 −1 Adding the above (d[n] h2[n]) to the answer in Part a, we get y[n] for this part which is shown on page 6. ↔ 7 Problem 2 continues on the following page
Part c. In order to use system H2 as a part of an edge detector, we would like to add an LTI system Hs whose unit sample response, hsn is shown below. System Hs smoothes out effect of noise on rn. The overall system can be represented as below hs(nI System h hsIn h2In y Provide a labeled sketch of the overall output ys [n], when pIn] and d(n] are exactly the same in part b ys[n 2
−2 1 Part c. In order to use system H2 as a part of an edge detector, we would like to add an LTI system Hs whose unit sample response, hs[n] is shown below. System Hs smoothes out effect of noise on x[n]. The overall system can be represented as below: 2 hs[n] −2 −1 0 1 n 1 1 System Hs System H2 p[n] + x[n] hs[n] h2[n] ys[n] d[n] Provide a labeled sketch of the overall output ys[n], when p[n] and d[n] are exactly the same as in Part b. ys[n] −7 −6 −5 −4 −3 −1 2 3 4 5 6 7 n 2 1 −2 −2 2 2 −3 8