Spherical fourier transform

1. What is the Fourier transform of a circle?
2. What is a spherical graph?
3. What are the limits of spherical polar coordinates?

What is the Fourier transform of a circle?

We note that the Fourier Transform of the function circle has a circular symmetry. It is composed of a central peak and a series of concentric rings of decreasing amplitudes. Image I-3 - Radial profile of the function represented on figure I-2. Figure I-3 represents a radial profile of this function.

What is a spherical graph?

A spherical graph is a graph in which every interval is antipodal. Spherical graphs are an interesting generalization of hypercubes (a graph G is a hypercube if and only if G is spherical and bipartite).

What are the limits of spherical polar coordinates?

Unique coordinates

r ≥ 0, 0° ≤ θ ≤ 180° (π rad), 0° ≤ φ < 360° (2π rad). However, the azimuth φ is often restricted to the interval (−180°, +180°], or (−π, +π] in radians, instead of [0, 360°).