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
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 Domain | Unilateral s domain | Bilateral 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
Relationship with Fourier Transform
See relationship with Fourier transform