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.