Coordinate conversion

[erdemath]

How would you define a proper Fourier domain in python? By converting cartesian (x,y) coordinates into polar coordinates (r,\phi)?

[Gribouillis]

I have a phd in mathematics and I don't understand the question.

[erdemath]

So do I. I edited the question.

I have a phd in mathematics and I don't understand the question.

[jefsummers]

Bachelor's in Math so I am hopeless.

However, I will offer a couple possible sources.
SciPy
Numpy FFTs

[Gribouillis]

You could perhaps describe the problem with more details. The question is very abstruse.

[erdemath]

One must be careful with ready-made. It is not about projecting the data onto the Fourier domain. It is about the Fourier domain itself.

Bachelor's in Math so I am hopeless.

However, I will offer a couple possible sources.
SciPy
Numpy FFTs

[erdemath]

No, it is not at all if you know what a domain of a function means. It is solely about defining Fourier domain on where the Fourier projected data is defined.

Maybe, I can state the question in other words; What would be proper frequency domain? Conversion of cartesian coordinates into polar coordinates?

You could perhaps describe the problem with more details. The question is very abstruse.

[Gribouillis]

A 17th century french author named Nicolas Boileau said

Ce que l'on conçoit bien s'énonce clairement, et les mots pour le dire arrivent aisément.

Unfortunately people don't speak such a great french today, so that automatic translators fail to render this in english, but it means approximately

Whatever is well conceived is clearly said, And the words to say it flow with ease.

May I suggest that the underlying problem is not well enough conceived? I hope you'll find a better helper than me...

[erdemath]

A 17th century french author named Nicolas Boileau said

Ce qui se conçoit bien s'énonce clairement, et les mots pour le dire arrivent aisément.

Unfortunately people don't speak such a great french today, so that automatic translators fail to render this in english, but it means approximately

Whatever is well conceived is clearly said, And the words to say it flow with ease.

May I suggest that the underlying problem is not well enough conceived? I hope you'll find a better helper than me...

I wish we had some auto-compiler here, like Latex. Let us consider the usual Euclidean domains (i.e., finite dimensional Hilbert spaces) \Omega_1 and
\Omega_2. Now, we define the following mapping

\Omega_1 --> \Omega_2
x --> f(x):=y

Which means, for any x \in \Omega_1, y := f(x) \in \Omega_2 . Here, the domains \Omega_1 and \Omega_2 are in the Euclidean space.
What I am questioning, what is the Fourier domain of \Omega_1 ? Is it simply the Fourier projection of the entire domain \Omega_1? Or, would it
still be fine if we consider polar coordinates as a conversion of \Omega_1?