HW6F13_sol

A we can write xn as xn and identify c 3 sin

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Unformatted text preview: 1.5 (d). π π n · cos n 3 6 1 π π = DTFT cos n + cos n 2 2 6 π π π π π = δ ω− +δ ω+ +δ ω− +δ ω+ 2 2 2 6 6 X (ej ω ) = DTFT cos 3 1 0.8 2.5 0.6 0.4 0.2 |X(ejω)| ∠ X(ejω) 2 1.5 0 −0.2 −0.4 1 −0.6 −0.8 0.5 −2 −1 0 ω∈[0,π] 1 −1 −2 2 342 −1 0 1 2 Problem 13.21. Find the DTFTs of the following sequences: (a). x(n) = sin( π n) 3 . n (b). x(n) = sin( π (n−1)) 3 . n−1 Solution. See Example 13.15 in the textbook. (a). We can write x(n) as x(n) = and identify ωc = π 3. π sin π n 3 · π 3 n 3 Then, we get X (ejω ) = π · rect ω π 3 where we defined the rectangular function rect(·) as 1, |ω | < ωc ω rect 0, ωc ωc ≤ |ω | ≤ π (b). Notice that this is a time-shifted version of part (a). We can immediately get X (ejω ) = π · re...
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This note was uploaded on 12/01/2013 for the course EE 113 taught by Professor Walker during the Fall '08 term at UCLA.

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