# Inverse laplace transform matlab

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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

## ilaplace(F)

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.

## ilaplace(F,transVar)

this function uses the transformation variable transVar instead of t.

## ilaplace(F,var,transVar)

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