In mathematics, the Laplace transform is a function involving integral transform named after its discoverer Pierre-Simon Laplace. It accepts a function of a real variable (t) (often time) to a function of a complex variable (s) (complex frequency). The Laplace transform is identical to the Fourier transform. While the Fourier transform of a function is a function of a real variable (frequency), the Laplace transform of a function is a complex function of a complex variable. Laplace transforms are generally restricted to functions of t with t ≥ 0. Similarly the inverse laplace transform is just the inverse of laplace transform. Mathematically it can be described as
The inverse Laplace transform of F = F(s) is:
Here, c is a suitable complex number.
Basically in MATLAB there are three functions that helps in solving inverse Laplace transforms
This function returns the Inverse Laplace Transform of F. By default, the independent variable in ilaplace is s and the transformation variable is t. If F does not contains any function, ilaplace uses the function symvar.
this function uses the transformation variable transVar instead of t.
this function uses the independent variable var and transformation variable transVar instead of s and t, respectively.
Various methods for solving different inverse Laplace transform can be seen below
- Inverse Laplace Transform of Symbolic Expression
- Default Independent Variable and Transformation Variable
- Inverse Laplace Transforms which Involve Dirac and Heaviside Functions
- Inverse Laplace Transform of Symbolic Function