Continue to Site

# Numerical Laplace !!!!!

Status
Not open for further replies.

#### ahmed osama

##### Full Member level 6
hi all

i need to know how to calc. laplace in numerical way , in other way i have the h(s) of a system and i want to see it step response using numerical way ????

Plz i am not asking for computer softwares like matlab but asking how such software do that !!!!! ??

thx all

you need abel software

look here for views from a proteus point of view 3rd party maker in france

abel can be used on its own as a simulator or as a language

http://lewebelectronique.free.fr/

and the other pages like dossier {documents} etc..

use babelfish to translate the french to local etc lingo

http://babelfish.altavista.com/

LAPLACE is a language that interpilates and extrapolates

http://mathworld.wolfram.com/FourierSeries.html

to gain outcomes from a set of variable's intergrated with a set of semi fixed transient values but also with respect to time

from all members will take ages to explain
in french or engish

you must be more specific

it's a big topic ...very.... and solves many problems

look for ebooks on the topic
if you cant find one
you may be able to ask for it in the ebooks section

Dear Ahmed,

Its simple numerical integration,

just substitute with your h(s) and multiply is by exp(-st) numerically for a good range of s eg, from 0 to 100 and integrate it numerically over that range with a very small step for s at different values of t.

If you're wondering what I'm talking about then you need to know there are numerical ways to calculate definite integrals as Simpson's or trapezoidal methods, where a curve is approximated by parabols or trapezoids respectively and their area is calculated, this is similar to doing the integral

Are you asking if there is a similar thing like DTFT (discrete Fourier Transform) for the laplace transform? I don't think it's difficult to define it, but it's a little hard to make sense of it. In other words, if this kind of idea does not appear so popular as DTFT, it's because there is not big use of it.

I think to find out how software does this you have to go and read the literature in the area of "numerical inversion of laplace transforms". Doing a google search results in lots of material. There is more than one method to do the inversion.

In particular, this one got my attention https://library.wolfram.com/infocenter/MathSource/2691/ This is for mathematica and even if you don't have mathematica you can download the free reader to view these packages. You can also search for some survey papers that compare different methods. Take a look at this for example

Dean G. Duffy, "On the numerical inversion of Laplace transforms: comparison of three new methods on characteristic problems from applications"
Source ACM Transactions on Mathematical Software (TOMS) archive
Pages: 333 - 359 , 1993

Hope this helps.

Best regards,
v_c

### ahmed osama

Points: 2
Numerical laplace trasform is used when the integral functions involved are imposibble or formidable to integrate.

In the context that you ask the way is too much easy. You should convert the transfer function H(s) into its state variable representation. When you do this you can simulate the step response by discretizing the obtained system. You can find a reference of this process in the book.

linear system theory ans design by Chi Tsong Chen.

A long time ago i red an article in a Apple magazine
that did numerical Laplace in basic.
The program itself wasn't that big.
I wil search for it and post it here.

if you are only asking for how to convert a impulse
response to step response then you simply
require to calculate h(s)/s and that will give
you the result. Since integration of impulse is
step and integration in time domain will result
in divison by s in lalplace domain

If x(t) is tie domain signal;
Then X(S) is laplace transform

X(S)=∫x(t)dt, where it integrates it rom -ve infinty to +ve infinty.

laplace using integral
so use the numerical of integral
enter to