How to do Fourier Integrals on the HP Prime?

[Stevetuc]

(12-08-2019 07:02 AM)Stevetuc Wrote:  

(12-07-2019 10:34 PM)medwatt Wrote:  Hello,

I want to do Fourier Integrals (not Fourier Series) on the Prime but there doesn't to be a function for that. I'm surprised that a calculator as powerful as the Prime doesn't have a built in function for this when there is one already for Laplace Transforms. The HP 50g can do Fourier Transforms. Is there some app out there that can add this functionality to the Prime ?

I tried this in cas mode

Code:


1/(√(2*π))*int(e^(i*w*t),t)

The result on max simplification

Code:


(-i)*√(2*π)*e^(i*t*w)/(2*π*w)

Which (I think ) is the deltadirac function and the correct result for fourier transform of 1 (see wolfram screenshots attached)
The prime doesnt recognise the above as a deltadirac (although there is a builtin Dirac) It may be helpful to define as a cas substitution to simplify results. I havent tried this yet.

Code:


1/(√(2*π))*int(Dirac(t)*e^(i*w*t),t,-(∞),∞)

Gives correct result of

Code:


1/√(2*π)

Comparing to wolfram.

Actually I see there is an e^-itw term missing in the result of my first example compared to wolfram, which may be the reason the cas doesn't recognise the result as a dirac()