I have a calculator with CAS ( https://en.wikipedia.org/wiki/Computer_algebra_system ) and in particular I have a Casio Algebra FX 2.0 Plus ( https://en.wikipedia.org/wiki/List_of_computer_algebra_systems ).
I need to compute Laplace / Zeta / Fourier Transform.
My calculator is able to calculate laplace transforms, in fact if I go in the CAS section and insert:
"$∫ (sinX * e-SX, X)$"
it gives me as a result:
" $-e^(-s·x)·(COS (x) + s · SIN (x)) / (s ^ 2 + 1) $"
then evaluating: $LIM (- e ^(-sx)·(COS (x) + s · SIN (x)) / (s ^ 2 + 1), x, ∞) - LIM (- e^(-s·x)·(COS (x) + s · SIN (x)) / (s ^ 2 + 1), x, 0 ) = 1 / (s ^ 2 + 1)$.
$ ℒ_x [sin (x) * step (x)] (s) = 1 / (s ^ 2 + 1)$.
I tried to do it even with more complex expressions, and I always get the correct result.
Unfortunately, I can not find a way to calculate the Z-Transform or the Fourier Transform, using the CAS of my calculator .
At this point I wondered if you knew:
OR 1) A method to calculate also Z-transform and Fourier-Transform by using the CAS of my calculator.
OR 2) Calculated the laplace transform of a function (since, as proven, my calculator is able to do this), then easily deduce from it the Z-Transform and the Fourier-Transform.
OR 3) Since my calculator also accepts C / C ++ programs, do you know any program in this language for the calculation of Fourier Transform / Zeta Transform? Thanks everyone in advance for the help.
Laplace Transform: https://en.wikipedia.org/wiki/Laplace_transform
Fourier Trnasform: https://en.wikipedia.org/wiki/Fourier_transform