Unitary Transform
The DFT is (or can be, through appropriate selection of scaling) a unitary transform, i.e., one that preserves energy. The appropriate choice of scaling to achieve unitarity is, so that the energy in the physical domain will be the same as the energy in the Fourier domain, i.e., to satisfy Parseval's theorem. (Other, non-unitary, scalings, are also commonly used for computational convenience; e.g., the convolution theorem takes on a slightly simpler form with the scaling shown in the discrete Fourier transform article.)
Read more about this topic: DFT Matrix
Famous quotes containing the word transform:
“It is necessary to turn political crisis into armed crisis by performing violent actions that will force those in power to transform the military situation into a political situation. That will alienate the masses, who, from then on, will revolt against the army and the police and blame them for this state of things.”
—Carlos Marighella (d. 1969)