# chapter6.pdf - Chapter 6 Laplace Transform 1 Definition of...

• No School
• AA 1
• 16

This preview shows page 1 - 6 out of 16 pages.

ELEC242: CT Signals and Systems Chapter 6 Laplace Transform 1. Definition of Laplace Transform 2. Unilateral vs. Bilateral Laplace Transform 3. Inverse Laplace Transform 4. Properties of Laplace Transform 5. Poles and zeros 6. LTIC System Analysis Sections: 6.1 – 6.10

Subscribe to view the full document.

ELEC242: CT Signals and Systems Laplace Transform: Definition Activity 1: Derive the following Laplace transform pair. ( ) ( ) = dt e t x s X st σ + σ π = j j st j ds e s X t x ) ( ) ( 2 1 Analysis equation: Synthesis equation: 1 ( ) with ROC: Re{ } L at e u t s a s a ←ί→ > +
ELEC242: CT Signals and Systems Computing DTFT: Exponential t 0 x 1 ( t ) Activity 1 (contd): Compute the Laplace transform of the decaying exponential function x 1 ( t ) = exp( at ) u ( t ), a ~ R + . Solution: Re{ s } Im{ s } a 0 ( ) { } { } Ϊ Ϊ Ω Ϊ Ϊ Ψ Χ > + = . Re for undefined Re for ) ( 1 a s a s a s s X

Subscribe to view the full document.

ELEC242: CT Signals and Systems Computing DTFT: Exponential Activity 2: Compute the Laplace transform of the decaying exponential function x ( t ) = exp( at ) u ( t ), a ~ R + . Solution: t 0 x ( t ) = e at u ( t ) ( ) { } { } Ϊ Ϊ Ω Ϊ Ϊ Ψ Χ < + = . Re for undefined Re for ) ( 1 a s a s a s s X Re{ s } 0 Im{ s } a
ELEC242: CT Signals and Systems Properties of ROC 1. The ROC consists of 2D strips parallel to the j -axis. 2. For a right sided function, the ROC takes the form Re{ s } > σ 0 consisting of the RHS of the s-plane. 3. For a left sided function, the ROC takes the form Re{ s } < σ 0 consisting of the LHS of the s-plane. 4. For a finite duration function, the ROC consists of the entire s-plane except for the possible deletion of the point s = 0. 5. For a double sided function, the ROC takes the form σ 1 < Re{s} < σ 2 and is a strip within the s-plane.

Subscribe to view the full document.

• Fall '19
• ω0t, σ0 consisting of the RHS of the s-plane

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern

Ask Expert Tutors You can ask 0 bonus questions You can ask 0 questions (0 expire soon) You can ask 0 questions (will expire )
Answers in as fast as 15 minutes