[amp_mcq option1=”{0, -2 + 2j, 2, -2 – 2j}” option2=”{2, 2 + 2j, 6, 2 – 2j}” option3=”{6, 1 – 3j, 2, 1 + 3j}” option4=”{6, -1 + 3j, 0, -1 – 3j}” correct=”option3″]<\/p>\n
The correct answer is $\\boxed{\\text{C}}$.<\/p>\n
The 4-point DFT of a discrete time sequence $x[n]$ is given by<\/p>\n
$$X[k] = \\sum_{n=0}^{3} x[n] e^{-j2\\pi nk\/N}$$<\/p>\n
where $N$ is the number of samples in the sequence. For the sequence $x[n] = {1, 0, 2, 3}$, we have<\/p>\n
$$X[0] = \\sum_{n=0}^{3} x[n] = 1 + 0 + 2 + 3 = 6$$<\/p>\n
$$X[1] = \\sum_{n=0}^{3} x[n] e^{-j2\\pi n\/4} = 1 – 0 + 2e^{-j\\pi} + 3e^{-j3\\pi} = 2 – 2j$$<\/p>\n
$$X[2] = \\sum_{n=0}^{3} x[n] e^{-j4\\pi n\/4} = 1 – 0 + 2e^{-j2\\pi} + 3e^{-j4\\pi} = 2 + 2j$$<\/p>\n
$$X[3] = \\sum_{n=0}^{3} x[n] e^{-j6\\pi n\/4} = 1 – 0 + 2e^{-j3\\pi} + 3e^{-j5\\pi} = 0 – 2j$$<\/p>\n
Therefore, the 4-point DFT of $x[n]$ is $\\boxed{\\text{C}}$.<\/p>\n
Option A is incorrect because $X[1]$ should be $2 – 2j$, not $0 – 2j$.<\/p>\n
Option B is incorrect because $X[2]$ should be $2 + 2j$, not $2 – 2j$.<\/p>\n
Option D is incorrect because $X[3]$ should be $0 – 2j$, not $-1 – 3j$.<\/p>\n","protected":false},"excerpt":{"rendered":"
[amp_mcq option1=”{0, -2 + 2j, 2, -2 – 2j}” option2=”{2, 2 + 2j, 6, 2 – 2j}” option3=”{6, 1 – 3j, 2, 1 + 3j}” option4=”{6, -1 + 3j, 0, -1 – 3j}” 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-55326","post","type-post","status-publish","format-standard","hentry","category-signal-processing","no-featured-image-padding"],"yoast_head":"\n