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Numerical Inverse Laplace Transform


Tucker McClure


Numerical approximation of the inverse Laplace transform for use with any function defined in "s".

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This set of functions allows a user to numerically approximate an inverse Laplace transform for any function of "s". The function to convert can be passed in as an argument, along with the desired times at which the function should be evaluated. The output is the response of the system at the requested times.

For instance, consider a ramp function.
f = @(s) 2/s^2;
t = [1 2 3 4 5]';
talbot_inversion(f, t)

The time response output is [2 4 6 8 10], as expected.

These methods can be used on problems of considerably more difficulty as well and are intended to approximate an inverse Laplace transform where an exact solution is unknown.

Two basic solvers (Euler and Talbot) are included, along with *symbolic* versions of those solvers. The symbolic solutions take substantially longer to calculate, but are capable of any desired accuracy. Also, the symbolic versions require the Symbolic Toolbox, whereas the basic versions do not.

Please see example_inversions.pdf or html/example_inversions.html to get started!

Required Products Symbolic Math Toolbox
MATLAB release MATLAB 8.0 (R2012b)
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Comments and Ratings (6)
03 Mar 2014 Yang


I would like to compute the inverse laplace transform of 1/(s-1i), which is exp(1i*t). But the programs are not working for this problem. Please help!

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04 Oct 2013 Deepak Ramaswamy

Deepak Ramaswamy

26 Apr 2013 Lee


15 Mar 2013 Tucker McClure

Tucker McClure

Hi Mohamed,

No, this is for continuous time only. However, Dr. Dan Ellis of Columbia University has an example of a numerical inverse z-transform written in MATLAB located here: http://www.ee.columbia.edu/~dpwe/e4810/matlab/s10/html/eval_z_transf.html

Note that this type of inversion is notoriously tricky to do numerically, as it requires very precise numbers. Working with the Symbolic Toolbox allows you to request arbitrary precision (e.g., 64 digits of precision).

Hope that helps!

- Tucker

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15 Mar 2013 Mohamed Yassin OUKILA

Mohamed Yassin OUKILA

Can we apply these functions to a discrete function?
Thank you :)

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20 Feb 2013 abdo mecha

abdo mecha


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