−1/8, so it "measures" how much "strength" there is at fractional frequency +1/8 in the signal. Recall that a matched filter compares the signal with a time reversed version of whatever we're looking for, so when we're looking for fracfreq. 1/8 we compare with fracfreq. −1/8 so that is why this row is a negative frequency. The next row is negative two cycles of a complex exponential, sampled in eight places, so it has a fractional frequency of −1/4, and thus "measures" the extent to which the signal has a fractional frequency of +1/4. The following summarizes how the 8-point DFT works, row by row, in terms of fractional frequency: 0 measures how much DC is in the signal −1/8 measures how much of the signal has a fractional frequency of +1/8 −1/4 measures how much of the signal has a fractional frequency of +1/4 −3/8 measures how much of the signal has a fractional frequency of +3/8 −1/2 measures how much of the signal has a fractional frequency of +1/2 −5/8 measures how much of the signal has a fractional frequency of +5/8 −3/4 measures how much of the signal has a fractional frequency of +3/4 −7/8 measures how much of the signal has a fractional frequency of +7/8 Equivalently the last row can be said to have a fractional frequency of +1/8 and thus measure how much of the signal has a fractional frequency of −1/8. In this way, it could be said that the top rows of the matrix "measure" positive frequency content in the signal and the bottom rows measure negative frequency component in the signal. 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.) Other properties For other properties of the DFT matrix, including its eigenvalues, connection to convolutions, applications, and so on, see the discrete Fourier transform article. A limiting case: The Fourier operator The notion of a Fourier transform is readily generalized. One such formal generalization of