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Mathematically, the Laplace Transform is represented as follows: | Mathematically, the Laplace Transform is represented as follows: | ||
| − | <center><math>X(s) = \int_{-\infty}^{\infty} x(t)e^{-st} dt\!</math> | + | <center><math>X(s) = \int_{-\infty}^{\infty} x(t)e^{-st} dt\!</math></center> |
Revision as of 16:12, 24 November 2008
The Laplace Transform
The Laplace Transform is a generalization of the Fourier Transform. Instead of considering only the imaginary axis, $ j\omega\! $, (as the Fourier Transform does) the Laplace Transform considers all complex values represented by the general complex variable $ s\! $. Take the following simple picture:
Fourier Transform: $ x(t) --> X(\omega)\! $ where $ \omega\! $ is a frequency.
Laplace Transform: $ x(t) --> X(s)\! $ where $ s\! $ is a complex variable.
Mathematically, the Laplace Transform is represented as follows:
