Fourier transform
04-13-2015, 10:08 PM (This post was last modified: 04-14-2015 05:12 PM by salvomic.)
Post: #1
 salvomic Senior Member Posts: 1,379 Joined: Jan 2015
Fourier transform
hi all,
a part of Fourier series coefficients (see here), there is a function in the Prime (or XCas) to get the Fourier Transform (not FFT) and its inverse?
See in Wolfram Alpha, for example...
If not, I need help to make a program.

We could calculate it via laplace() (Laplace transform), but we need the "bilateral laplace transform" and I don't know how to get it with the Prime...
F[f(t)] == bilateral-L[f(t)] where $$s=i\omega$$

Thank you
Salvo

EDIT:
the general equation should be
$\int_{-\infty }^{\infty }f(x) e^{-i\omega t}dt$
but with Prime I get often "undef" and if I set "complex" in CAS I get "Limit: Max order reached or unable to make series expansion Error: Bad argument"

∫aL√0mic (IT9CLU) :: HP Prime 50g 41CX 71b 42s 39s 35s 12C 15C - DM42, DM41X - WP34s Prime Soft. Lib
04-14-2015, 08:44 PM (This post was last modified: 04-15-2015 05:50 PM by salvomic.)
Post: #2
 salvomic Senior Member Posts: 1,379 Joined: Jan 2015
RE: Fourier transform
there is a way to solve an integral like that in the attached image and to avoid the errors that Terminal shows?

the integral is a tentative to get Fourier transform of $$\frac{1}{1+t^{2}}$$, that's $$\sqrt{\frac{\pi}{2}}e^{-|\omega|}$$ ...

***
Also, there is a way to solve laplace($$\frac{1}{1+t^{2}}$$, t, s) without getting "Limit: Max order reached or unable to make series expansion Error: Bad argument" error?

Attached File(s) Thumbnail(s)

∫aL√0mic (IT9CLU) :: HP Prime 50g 41CX 71b 42s 39s 35s 12C 15C - DM42, DM41X - WP34s Prime Soft. Lib
10-26-2015, 05:00 AM (This post was last modified: 10-26-2015 05:02 AM by Archanus.)
Post: #3
 Archanus Junior Member Posts: 49 Joined: Dec 2014
RE: Fourier transform
Hey Salvomic

Is there a way to implement Fourier Transform to HP Prime? It has been a long time since nobody view this post :/

Electrical Engineering students need a lot this powerful Integral Transform

Casio ClassPad (I & II) and TI Nspire CX CAS has Fourier Transform. I'm so sad to know anything about a new firmware that could provide almost all the tools for Students for System Information, Software & Electrical Engineering ...They prefer implement functions to Statistics Field and Geometry ):

And sorry for the complain but all HP users are anxious to see our HP Prime be even more powerful...
10-26-2015, 07:27 AM
Post: #4
 salvomic Senior Member Posts: 1,379 Joined: Jan 2015
RE: Fourier transform
(10-26-2015 05:00 AM)Archanus Wrote:  [color=#0000CD][b]Hey Salvomic

Is there a way to implement Fourier Transform to HP Prime? It has been a long time since nobody view this post :/

...

hi Arcanus,

I made a program to calculate the Fourier coefficient, but now Prime has inside the a_n, b_n c_n coefficients by itself, I don't remember other improvements about this argument...

Salvo

∫aL√0mic (IT9CLU) :: HP Prime 50g 41CX 71b 42s 39s 35s 12C 15C - DM42, DM41X - WP34s Prime Soft. Lib
10-26-2015, 02:17 PM
Post: #5
 Tim Wessman Senior Member Posts: 2,239 Joined: Dec 2013
RE: Fourier transform
(10-26-2015 05:00 AM)Archanus Wrote:  [color=#0000CD][b]Hey Salvomic
Electrical Engineering students need a lot this powerful Integral Transform

Please explain what is missing if you still think something is no there that should be. You have 3 different varieties of fourier transforms at this moment.

TW

Although I work for the HP calculator group, the views and opinions I post here are my own.
10-26-2015, 06:39 PM
Post: #6
 Archanus Junior Member Posts: 49 Joined: Dec 2014
RE: Fourier transform
(10-26-2015 07:27 AM)salvomic Wrote:
(10-26-2015 05:00 AM)Archanus Wrote:  Hey Salvomic

Is there a way to implement Fourier Transform to HP Prime? It has been a long time since nobody view this post :/

...

hi Arcanus,

I made a program to calculate the Fourier coefficient, but now Prime has inside the a_n, b_n c_n coefficients by itself, I don't remember other improvements about this argument...

Salvo

[color=#0000CD][b]Hey !

Yes dear friend, but I'm asking for Fourier Transform with Integrals

You made a nice program to find the coeff of the Fourier Series, Trigonometric & Exponential
10-26-2015, 06:44 PM
Post: #7
 salvomic Senior Member Posts: 1,379 Joined: Jan 2015
RE: Fourier transform
(10-26-2015 06:39 PM)Archanus Wrote:  ...
You made a nice program to find the coeff of the Fourier Series, Trigonometric & Exponential [/b][/color]

thank you for compliments :-)
I hope also to have that, as I wrote in the original post.
Tim says well that the Prime has all the other forms of Fourier transform (that are sure more used) but this one would complete the series...

Salvo

∫aL√0mic (IT9CLU) :: HP Prime 50g 41CX 71b 42s 39s 35s 12C 15C - DM42, DM41X - WP34s Prime Soft. Lib
10-26-2015, 06:47 PM
Post: #8
 Archanus Junior Member Posts: 49 Joined: Dec 2014
RE: Fourier transform
(10-26-2015 02:17 PM)Tim Wessman Wrote:
(10-26-2015 05:00 AM)Archanus Wrote:  Hey Salvomic
Electrical Engineering students need a lot this powerful Integral Transform

Please explain what is missing if you still think something is no there that should be. You have 3 different varieties of fourier transforms at this moment.

[b][color=#0000CD]For Example implement Hilbert Transform, Spectrum Analysis, Multiple Variable Equation Solve (This feature is been requested a long time ago), more stable the firmware and the OS, Hartley transform, Two-sided Laplace transform, Abel transform, Discrete Plots, and many more wishes of the HP Users
10-26-2015, 07:01 PM
Post: #9
 Archanus Junior Member Posts: 49 Joined: Dec 2014
RE: Fourier transform
(10-26-2015 06:44 PM)salvomic Wrote:
(10-26-2015 06:39 PM)Archanus Wrote:  ...
You made a nice program to find the coeff of the Fourier Series, Trigonometric & Exponential [/b][/color]

thank you for compliments :-)
I hope also to have that, as I wrote in the original post.
Tim says well that the Prime has all the other forms of Fourier transform (that are sure more used) but this one would complete the series...

Salvo

You're welcome

Hey For the Coeff An that is: https://upload.wikimedia.org/math/8/c/2/...7b6ceb.png

In the HP Prime: fourier_bn(t,t,2,-1,1) ; in other words that function to implement in Fourier Series but the Period is from -1 to 1, so it's 2... I use bn because it's an odd function so a0 & an == 0