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Laplace Transform: <math>x(t) --> X(s)\!</math> where <math>s\!</math> is a complex variable. | Laplace Transform: <math>x(t) --> X(s)\!</math> where <math>s\!</math> is a complex variable. | ||
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| + | Mathematically, the Laplace Transform is represented as follows: | ||
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| + | <math>X(s) = \int_{-\infty}^{\infty}\!</math> | ||
Revision as of 16:11, 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:
$ X(s) = \int_{-\infty}^{\infty}\! $
