HW6F13_sol

Notice that xn 64 4n1 un 1 which is a left sided

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: |X (ejω )| = 1 3 82 81 − 2 9 ∠X (ejω ) = −ω − arctan , · cos(ω ) sin(ω ) 9 − cos(ω ) (c). Notice that x(n) = −64 · 4−n−1 u(−n − 1) which is a left-sided sequence. Its z -transform is given by X (z ) = and its ROC is given by −64 · z 1−4·z 1 4 Since on every point of the unit circle the X (z ) diverges, its DTFT does not exist. 0 ≤ |z | &lt; 338 Problem 13.11. Find the DTFTs of the following sequences: π 3n (a). x(n) = cos π 3n (b). x(n) = cos π 3n (c). x(n) = cos π 3n + 2j · sin (d). x(n) = cos π 3n · cos sin − 2π 3 . . π 6n π 6n . . In each case, plot the magnitude and phase of the DTFT. Solution. (a). π π n sin n 3 3 2π 1 sin n = DTFT 2 3 −jπ 2π 2π = δ ω− −δ ω+ 2 3 3 π 2π π 2π = δ ω− e−j π/2 + δ ω + 2 3 2 3 X (ejω ) = DTFT cos 3 ej π/2 2 1.5 2.5 1 0.5 |X(ejω)| ∠ X(e...
View Full Document

Ask a homework question - tutors are online