 The Edelman algorithm works equally well for sparse and non-sparse data, since it is based on the compressibility (rank deficiency) of the Fourier matrix itself rather than the compressibility (sparsity) of the data.Conversely, if the data are sparse—that is, if only "K" out of "N" Fourier coefficients are nonzero—then the complexity can be reduced to O("K"log("N")log("N"/"K")), and this has been demonstrated to lead to practical speedups compared to an ordinary FFT for "N"/"K" > 32 in a large-"N" example ("N" = 222) using a probabilistic approximate algorithm (which estimates the largest "K" coefficients to several decimal places).Even the "exact" FFT algorithms have errors when finite-precision floating-point arithmetic is used, but these errors are typically quite small; most FFT algorithms, e.g.