{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# lt1 - Boise State University Department of Electrical and...

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

Boise State University Department of Electrical and Computer Engineering ECE225 – Circuit Analysis and Design The Laplace Transform I Reading Assignment : Read Sections 15.2-15.3 Lecture Objectives : 1. To define the Laplace transform. 2. To review some properties of Laplace transforms. 3. To derive the Laplace transforms of elementary time functions. Example of a Transform: The Logarithm Transform Real Domain -→ Real Domain a ln -→ x = ln a b ln -→ y = ln b c = ab = e ln z e = ln - 1 ←- z = x + y = ln a + ln b = ln ab Definition of the (One-Sided) Laplace Transform : L { f ( t ) } = Z 0 - f ( t ) e - st dt = F ( s ) Notes : 1. The Laplace integral is integrated over time starting shortly time t = 0. (This is indicated by the notation 0 - which means 0 - ² , ² being an arbitrarily small number.) The reason for using 0 - instead of 0 will become apparent later on. 2. The variable s is a complex variable. Thus the Laplace domain (or s-domain) represents functions of a complex number s = σ + . 3. The Laplace integral defined above will converge for a particular s if Z 0 - | f ( t ) e - st | dt = Z 0 - | f ( t ) | e - σt dt < 4. In particular, a function that does not grow faster than an exponential,

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 ]}

### 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