ECE634S09_L7_LaplaceTransformProperties

ECE634S09_L7_LaplaceTransformProperties - ECE634 Signals...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
ECE634 Signals and Systems II, Spring 2009 - Lecture 7, February 6 Daniel S. Brogan 1 4.2 Some Properties of the Laplace Transform: Table on p.369 in the text Time shifting For () () ( ) xtut X s , ( ) ( ) ( ) 0 00 st x ttu tt Xse −− for 0 0 t Exercise E4.3: Find the Laplace Transform of the signal illustrated in the figure below First find () x t () () ( )( ) ( ) ( ) 32 2 23 3 xt tut t ut t =− + Since these are all time-shifted ramps, the time shifting property can be combined with 2 1 tu t s to yield 2 3 22 2 2 11 1 1 1 3 2 s ss s X se e e e s s + = + Exercise E4.4: Find the inverse Laplace transform of ( ) 2 3 12 s e Xs = + First find x t without time shifting… ( ) 3 1 2 AB s s =+ −+ + 1 3 1 2 s A s = == + 2 3 1 1 s B s = t 0 2 2 x ( t ) 3 1
Background image of page 1

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

View Full DocumentRight Arrow Icon
ECE634 Signals and Systems II, Spring 2009 - Lecture 7, February 6 Daniel S. Brogan 2 () ( ) 31 1 12 1 2 ss s s =− −+ + Without time shifting this becomes… () () 2 tt x te e u t ⎡⎤ ⎣⎦ With time shifting this becomes… 22 2 2 t t xt e e ut −− Frequency shifting For () () ( ) xtut X s , ( ) ( ) ( ) 0 0 st xtute X s s ⇔− Example: Derive pair 9b in Table 4.1 (p.344) from pair 8b and the frequency shifting
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 03/05/2009 for the course ECE 651 taught by Professor Messner during the Spring '09 term at New Hampshire.

Page1 / 5

ECE634S09_L7_LaplaceTransformProperties - ECE634 Signals...

This preview shows document pages 1 - 3. Sign up to view the full document.

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