The predecessor of the DFT is the finite Fourier transform, and window functions were "always an odd number of points and exhibit even symmetry about the origin". In that case, the DTFT is entirely real-valued. When the same sequence is shifted into a DFT data window, [ 0 ≤ ≤ n ≤ ≤ N ] , the DTFT becomes complex-valued except at frequencies spaced at regular intervals of 1 / N . Thus, when sampled by an N -length DFT, the samples (called DFT coefficients) are still real-valued. An approximation is to truncate the N +1-length sequence (effectively w [ N ] = 0 ), and compute an N -length DFT. The DTFT (spectral leakage) is slightly affected, but the samples remain real-valued. The terms DFT-even and periodic refer to the idea that if the truncated sequence were repeated periodically, it would be even-symmetric about n = 0 , and its DTFT would be entirely real-valued. But the actual DTFT is generally complex-valued, except for the N DFT coefficients. Spectral plots like those at § Examples of window functions, are produced by sampling the DTFT at much smaller intervals than 1 / N and displaying only the magnitude component of the complex numbers.