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### Highlights from Numerical Inverse Laplace Transform

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# Numerical Inverse Laplace Transform

### Tucker McClure (view profile)

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

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Description

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
MATLAB release MATLAB 8.0 (R2012b)
21 Jul 2016 Fatih Olmez

### Fatih Olmez (view profile)

09 May 2016 Christian Reece

### Christian Reece (view profile)

18 Mar 2016 H Xue

### H Xue (view profile)

09 Sep 2015 Will Mansouri

### Will Mansouri (view profile)

Hi tucker

Thank you. Would your inverse laplace result in a solution that can be used as a starting condition and still maintain the same solution?

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04 Jun 2015 Mohamed Yassin OUKILA

### Mohamed Yassin OUKILA (view profile)

Hi Tucker,

Thank you very much for the help. I have just read your answer and I it helped me a lot.

Mohamed

26 Apr 2015 Günter Pfeifer

### Günter Pfeifer (view profile)

Doesn't work very well with
periodic functions like:

F1 = @(s) 1 / (s * (1 + exp(-s)));
or
F1 = @(s) (1 - exp(-s) .* (s + 1)) ./ (s.^2 .* (1 - exp(-s)));

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03 Mar 2014 Yang

### Yang (view profile)

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

26 Apr 2013 Lee

### Lee (view profile)

15 Mar 2013 Tucker McClure

### Tucker McClure (view profile)

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 (view profile)

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

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20 Feb 2013 abdo mecha

THAANKS

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