The one-sided (unilateral) *Laplace transform*
of a signal
is defined as

- time in seconds
- is a complex variable
- Appropriate for
*causal*signals

When evaluated along the
axis (*i.e.*,
), the
Laplace Transform reduces to the unilateral *Fourier transform*:

Thus, the Laplace transform generalizes the Fourier transform from the real line (the frequency axis) to the entire complex plane.

The Laplace Transform can also be seen as the Fourier transform of an

Download Laplace.pdf

Download Laplace_2up.pdf

Download Laplace_4up.pdf

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Center for Computer Research in Music and Acoustics (CCRMA), Stanford University

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