The appeal of DFT-symmetric windows is explained by the popularity of the fast Fourier transform (FFT) algorithm for implementation of the DFT, because truncation of an odd-length sequence results in an even-length sequence. Their real-valued DFT coefficients are also an advantage in certain esoteric applications where windowing is achieved by means of convolution between the DFT coefficients and an unwindowed DFT of the data. In those applications, DFT-symmetric windows (even or odd length) from the Cosine-sum family are preferred, because most of their DFT coefficients are zero-valued, making the convolution very efficient.