{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

HW6F13_sol

HW6F13_sol - EE 113 Digital Signal Processing Solutions for...

This preview shows pages 1–4. Sign up to view the full content.

EE 113 Digital Signal Processing Solutions for Homework VI Instructor: Professor Ali H. Sayed TA: Zaid Towfic, Xiaochuan Zhao November 12, 2013

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Problem 13.9. Find the DTFTs of the following sequences: (a). x ( n ) = ( 1 2 ) n 1 u ( n + 1) . (b). x ( n ) = ( 1 3 ) 2 n 1 u ( n 1) . (c). x ( n ) = ( 1 4 ) n 2 u ( n 1) . In each case, ±nd expressions for the magnitude and phase of the DTFT. Solution. (a). Notice that x ( n ) = 4 · p 1 2 P n +1 u ( n + 1) Thus, we get X ( e ) = 4 e 1 1 2 e = 4 · exp( ) r 5 4 cos( ω ) · exp ± j arctan ± sin( ω ) 2 cos( ω ) ²² where the amplitude and phase are given by | X ( e ) | = 4 r 5 4 cos( ω ) , X ( e ) = ω arctan p sin( ω ) 2 cos( ω ) P (b). Notice that x ( n ) = 1 3 · p 1 9 P n 1 u ( n 1) Thus, we get X ( e ) = 1 3 · e 1 1 9 e = 1 3 · exp( ) r 82 81 2 9 · cos( ω ) · exp ± j arctan ± sin( ω ) 9 cos( ω ) ²² where the amplitude and phase are given by | X ( e ) | = 1 3 r 82 81 2 9 · cos( ω ) , X ( e ) = ω arctan p sin( ω ) 9 cos( ω ) P (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 ) = 64 · z 1 4 · z and its ROC is given by 0 ≤ | z | < 1 4 Since on every point of the unit circle the X ( z ) diverges, its DTFT does not exist. 338
Problem 13.11. Find the DTFTs of the following sequences: (a). x ( n ) = cos ( π 3 n ) sin ( π 3 n ) .

This preview has intentionally blurred sections. Sign up to view the full version.

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

{[ snackBarMessage ]}

Page1 / 9

HW6F13_sol - EE 113 Digital Signal Processing Solutions for...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online