How to do Fourier Integrals on the HP Prime?

[Stevetuc]

(12-09-2019 09:54 PM)medwatt Wrote:  

(12-09-2019 08:45 PM)Stevetuc Wrote:  Yes indeed. I shared the above code fragment to make that fact clear!
You may have to move back to TI or Casio, assuming you have an app that meets your needs or Wolfram.

Thanks, man. I appreciate the effort. There's a package for Laplace Transform for the Ti-89 which I've modified to do the Fourier Transform. The Casio Classpad II can do FT natively but I'm not a fan of it as it is barely has any hardware keys and therefore makes no sense buying it when you can just install any one of the myriad calculator applications on Android.

I took a look at the classpad app. It has an impressive range of options for the fourier transform, allowing interactive input of the indep var and parameter and different style of formulation such as pure math, physics and signal processing.
Results agree with wolfram and it recognises that for a dc signal, or a unit pulse as T/2 -> inf that the sinc function -> deltadirac.
   

That isnt possible currently on the prime. If you take the fourier integral of a pulse -T/2 to +T/2 in the limit as T ->inf the result is undefined.

Code:

∫(e^(-i*w*t),t,-τ/2,τ/2)

gives

Code:

(i*e^((−i)*w*τ/2)+(−i)*e^(i*w*τ/2))/w

which are sinc functions, but if you take the limit as τ ->inf the result is undef. The classpad and wolfram both recognise the limiting case of a sinc fn to be a delta.

I also looked at ti89 function lapl.89f.
https://www.ticalc.org/archives/files/fi...44290.html
It looks pretty basic (nopun).

Code:


[….]
If inString(string(∫(fx*e^(-p*var),var)),"∫")=0 Then 
∫(fx*e^(-p*var),var)->lf
limit(lf,var,∞)->ilf
[….]

Is that the program you modified? Maybe this could be ported to the prime or the hpcalc.org spect program I posted earlier could be modified to use integral form instead of single sided laplace.