[amp_mcq option1=”5, 2″ option2=”6, 2″ option3=”6, 1″ option4=”5, 3″ correct=”option3″]<\/p>\n
The correct answer is $\\boxed{\\text{(A) 5, 2}}$.<\/p>\n
The output sequence $y[n]$ is given by the convolution of the input sequence $x[n]$ and the impulse response $h[n]$:<\/p>\n
$$y[n] = \\sum_{k=-\\infty}^{\\infty} x[k] h[n-k]$$<\/p>\n
In this case, we have:<\/p>\n
$$y[0] = x[0] h[0] + x[2] h[-2] = 1 \\cdot 1 + 1 \\cdot 2 = 3$$<\/p>\n
$$y[1] = x[0] h[1] + x[2] h[-1] = 1 \\cdot -1 + 1 \\cdot 0 = -1$$<\/p>\n
$$y[2] = x[0] h[2] + x[2] h[0] = 1 \\cdot 2 + 1 \\cdot 1 = 3$$<\/p>\n
$$y[n] = 0 \\text{ for } n \\neq 0, 1, 2$$<\/p>\n
Therefore, the number of nonzero samples in the output sequence is 5, and the value of $y[2]$ is 3.<\/p>\n
Option (B) is incorrect because the number of nonzero samples in the output sequence is 5, not 6.<\/p>\n
Option (C) is incorrect because the value of $y[2]$ is 3, not 1.<\/p>\n
Option (D) is incorrect because the number of nonzero samples in the output sequence is 5, not 3.<\/p>\n","protected":false},"excerpt":{"rendered":"
[amp_mcq option1=”5, 2″ option2=”6, 2″ option3=”6, 1″ option4=”5, 3″ correct=”option3″]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[959],"tags":[],"class_list":["post-58898","post","type-post","status-publish","format-standard","hentry","category-signal-processing","no-featured-image-padding"],"yoast_head":"\n