On 2D Inverse Problems/Fourier coordinates

From Wikibooks, open books for an open world
Jump to: navigation, search
Let  be a not unit N'th root of unity, i.e. .

The discrete Fourier transform 's given by the symmetric Vandermonde matrix:
For example,
Exercise (*). The square of the Fourier transform is the identity transform:
Exercise (*). If an e-network is rotation invariant, then so 's the conductivity equation and the Dirichlet-to-Neumann map is diagonal in the Fourier coordinates (the column vectors of the matrix.