20102ee113_1_hw5_sol_2010

20102ee113_1_hw5_sol_2010 - EE113: Digital Signal...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

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

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: EE113: Digital Signal Processing Spring 2010 Prof. Mihaela van der Schaar Homework #5 Solutions 10.2 We re-write ? ( ? ) as ? ( ? ) = 6 ? + 3 − 2 ? − 1 6 ? 2 − 5 ? + 1 = ? − 1 6 ? 2 + 3 ? − 2 6 ? 2 − 5 ? + 1 = ? − 1 (1 + 8 ? − 3 6 ? 2 − 5 ? + 1 ) We let ? ′ ( ? ) = 8 ? − 3 6 ? 2 − 5 ? + 1 , and it can be written as ? ′ ( ? ) = 1 3 ? − 1 + 2 2 ? − 1 Hence, ? ( ? ) = ? − 1 (1 + 1 / 3 ? − 1 / 3 + 1 ? − 1 / 2 ), and ? ( ) is as following: (a) ROC: ∣ ? ∣ < 1 / 3 ? ( ) = ( − 1) − 1 3 ( 1 3 ) − 2 ( − + 1) − ( 1 2 ) − 2 ( − + 1) = ( − 1) − ( 1 3 ) − 1 ( − + 1) − ( 1 2 ) − 2 ( − + 1) (b) ROC: 1 / 3 < ∣ ? ∣ < 1 / 2 ? ( ) = ( − 1) + 1 3 ( 1 3 ) − 2 ( − 2) − ( 1 2 ) − 2 ( − + 1) = ( − 1) + ( 1 3 ) − 1 ( − 2) − ( 1 2 ) − 2 ( − + 1) (c) ROC: ∣ ? ∣ > 1 / 2 ? ( ) = ( − 1) + 1 3 ( 1 3 ) − 2 ( − 2) + ( 1 2 ) − 2 ( − 2) = ( − 1) + ( 1 3 ) − 1 ( − 2) + ( 1 2 ) − 2 ( − 2) 11.2. Correct answer is (a). Recall that an LTI system is causal if and only if the ROC of its transfer function includes the exterior of a disc for some radious < ∞ , including ? = ∞ ....
View Full Document

This note was uploaded on 06/06/2010 for the course EE 113 taught by Professor Walker during the Spring '08 term at UCLA.

Page1 / 5

20102ee113_1_hw5_sol_2010 - EE113: Digital Signal...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online