For an integer *N*, let be a not unit *N'*th root of unity.

- .

We consider the following discrete **Fourier transform** given by the symmetric **Vandermonde matrix**:

For example,

The square of the Fourier transform is the identity transform:

**Exercise (*).** If a network w/conductivity is rotation invariant then its Dirichlet-to-Neumann operator is diagonal in the Fourier coordinates. (Hint) The -harmonic functions commute w/rotations.