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Consider the following length-16 signal: x(n) = 0.5 + 2 sin(0.5tn)+1.5 cos (TTn), n = 0, 1,..., 15 a. Determine the DTFT X (w) of this finite sequence, and sketch it roughly versus w in the range 0 < w < 21. [Hint: Remember that each spectral line gets replaced by the rectangular window's frequency response.] b. Without performing any DFT or FFT computations, determine the 16-point DFT of this sequence. Then, determine the 8-point DFT of the same sequence. c. Place the 16-point DFT values on the graph of X (w) of part (a).

Consider the following length-16 signal: x(n) = 0.5 + 2 sin(0.5tn)+1.5 cos (TTn), n = 0, 1,..., 15 a. Determine the DTFT X (w) of this finite sequence, and sketch it roughly versus w in the range 0 < w < 21. [Hint: Remember that each spectral line gets replaced by the rectangular window's frequency response.] b. Without performing any DFT or FFT computations, determine the 16-point DFT of this sequence. Then, determine the 8-point DFT of the same sequence. c. Place the 16-point DFT values on the graph of X (w) of part (a).

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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Consider the following length-16 signal: x(n)= 0.5 + 2 sin(0.5tn)+1.5 cos (Tn), n = 0, 1,..., 15 a. Determine the DTFT X (w) of this finite sequence, and sketch it roughly versus w in the range 0 < w < 27. [Hint: Remember that each spectral line gets replaced by the rectangular window's frequency response.] b. Without performing any DFT or FFT computations, determine the 16-point DFT of this sequence. Then, determine the 8-point DFT of the same sequence. c. Place the 16-point DFT values on the graph of X (w) of part (a).
Transcribed Image Text:Consider the following length-16 signal: x(n)= 0.5 + 2 sin(0.5tn)+1.5 cos (Tn), n = 0, 1,..., 15 a. Determine the DTFT X (w) of this finite sequence, and sketch it roughly versus w in the range 0 < w < 27. [Hint: Remember that each spectral line gets replaced by the rectangular window's frequency response.] b. Without performing any DFT or FFT computations, determine the 16-point DFT of this sequence. Then, determine the 8-point DFT of the same sequence. c. Place the 16-point DFT values on the graph of X (w) of part (a).
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