The unilateral Laplace transform is only appropriate for transforming causal signals. By contrast, bilateral Laplace transform can handle all kinds of signals.

The bilateral Laplace transform of a function is defined as the following:

Properties

The properties of bilateral Laplace transform is very similar to the properties of unilateral Laplace transform, but there are some important differences.

In particular, the time differentiation property is simpler with bilateral Laplace transform:

Time DomainUnilateral s domainBilateral s domain

Inverse Transform

See also: inverse Laplace transform

Unlike the unilateral Laplace transform, the inverse of the bilateral Laplace transform is not unique. In other words, given a function in the complex frequency domain, there are multiple possible inverse transforms unless a region of convergence is specified.

Relationship with Fourier Transform

See relationship with Fourier transform

See Also