# Tuto9_sol - The ROC of the second expression is Re{s}...

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

EE3210 Tutorial 9 (Solution) 1. 5 } Re{ , 5 ) 1 ( ) ( ) 5 ( ) 5 ( 1 5 > + = = = + + s s e dt e dt e t u e s X s t s st t 2. a) No. From Property 3 of ROC for Laplace transform, for a finite-length signal, the ROC is the entire s -plane. b) Yes. Since the signal is absolutely integrable or stable, the ROC must include the j ω -axis. Furthermore, X ( s ) has a pole at s = 2. Therefore, one valid ROC is Re{ s } < 2, which corresponds to a left-sided signal. c) No. Since the signal is absolutely integrable or stable, the ROC must include the j -axis. Furthermore, X ( s ) has a pole at s = 2. Therefore, we can never have an ROC of the form Re{ s } > α where is a negative number. d) Yes. Since the signal is absolutely integrable or stable, the ROC must include the j -axis. Furthermore, X ( s ) has a pole at s = 2. Therefore, one valid ROC is < Re{ s } < 2, where is a negative number. 3. Let 3 4 12 7 ) 2 ( 2 ) ( 2 + + + = + + + = s B s A s s s s X We have A = 4 and B = 2. The ROC of the first expression is Re{s} > -4.

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.

Unformatted text preview: The ROC of the second expression is Re{s} &gt; -3. (Note: the intersection of the above two regions should be the same as the ROC of the original expression.) Taking the inverse Laplace transform, we obtain ) ( 2 ) ( 4 ) ( 3 4 t u e t u e t x t t − − − = . 4. The Laplace transforms of x 1 ( t ) and x 2 ( t ) are 2 } Re{ , 2 1 ) ( 1 − &gt; + = s s s X 3 } Re{ , 3 1 ) ( 2 − &gt; + = s s s X Using the time-shifting and time-scaling properties, we obtain 2 } Re{ , 2 ) ( ) 2 ( 2 1 2 1 − &gt; + = ↔ − − − s s e s X e t x s s L 3 } Re{ , 3 ) ( ) 3 ( 3 2 3 2 &lt; + − = − ↔ + − − − s s e s X e t x s s L . Using the convolution property yields 3 } Re{ 2 , 3 2 ) ( 3 2 &lt; &lt; − ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ + − ⋅ ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ + = − − s s e s e s Y s s...
View Full Document

## Tuto9_sol - The ROC of the second expression is Re{s}...

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

View Full Document
Ask a homework question - tutors are online