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.