What are the
spherical harmonics used for? They are most often used to create an
orthonormal basis for a function on the unit
sphere. This is because a function on the sphere with
bandwidth L can be represented as a sum of the spherical harmonics of up to order
L. A spherical
fourier transform or
wavelet transform is used to determine the spherical harmonic coefficients, which can be operated on (
filtered) before the inverse transform. The most common filtering operation on the spherical harmonics is a
triangular truncation, or
high-pass filter, where harmonics at or above order N are eliminated.
An example wave function having such properties are spherically expanding electromagnetic waves. Spherical harmonics are useful in performing near to far-field transforms on such wave functions, as well as filtering and interpolation.