How can I plot a function in Laplace domain using my time-domain data?

[edlewis]

This is not a Bode plot question, but similar.

I have data on the laplace transform of a tracer response at different times, "t". I want to plot the response against "s".

Since the Laplace transform of t is 1/s^2, do I convert to "s" by s=(1/t)^.5?

 

[Atrus]

At the beginning, sorry for both my English and lousy typing skills, but my knowledge of TeX is... well, nonexistent and I do my best with English :)

If I understood correctly, you have a function f(t) which is your time-domain response, and you want to plot it's s-domain representation in Laplace variable s? Or is it vice versa?

In any case, making a plain substitute of the time variable (t) or the frequency variable (s) won't give a correct answer.

Theoretically, Laplace transform of a function f is
Integral(0 -> +Inf) (f(t)e^(-s*t)dt)

In practice, you would use pre-made tables of standard terms like e^(a*t), t, sin(a*t) and such. You then transform your function into the sum of terms given in the table and then substitute time-domain terms into s-domain.

E.g.

f(t) = sin(2*t)*cos(3*t)

f(t) = 0.5 * sin(5*t) - 0.5*sin(t)

as Laplace(sin(a*t)) = a/(s^2+a^2)

F(s) = Laplace(f(t)) = 0.5*5/(s^2+25)-0.5/(s^2+1)

You can collect the terms to make it into a single function which you can then plot against s.

If your function can not be disassembled into terms found in tables of Laplace transform, well, then you'll have to calculate above integral transform by hand.

Hope I helped

P.S. most of calculus or engineering math handbooks have Laplace transform tables in their appendices.

 

[ravenprp]

To plot a function in Laplace domain using time-domain data, you can follow these steps:

1. Convert the time-domain data to the Laplace domain using the Laplace transform. This will give you a function in terms of the variable "s" instead of "t".

2. Once you have the function in Laplace domain, you can plot it against the variable "s". This will give you a graph that represents the function in the Laplace domain.

3. If you have data on the Laplace transform of a tracer response at different times, you can use the inverse Laplace transform to convert it back to the time domain. This will give you a function in terms of "t" again.

4. Now, you can plot the time-domain function against the variable "t" to compare it with the Laplace domain function plotted against "s".

5. To convert the Laplace domain function to "s", you can use the formula s=(1/t)^0.5, as you mentioned. This will give you the corresponding values of "s" for the function at different times.

6. Finally, you can plot the function in Laplace domain against "s" using the values obtained from the conversion. This will give you a graph that represents the function in the Laplace domain using your time-domain data.

In summary, to plot a function in Laplace domain using time-domain data, you will need to convert the data to the Laplace domain, plot the function against "s", and then convert it back to the time domain for comparison. Using the formula s=(1/t)^0.5, you can convert the function to "s" and plot it against this variable. I hope this helps.