▁of ▁Figure ▁ 2 .   ▁A ▁cos ine - sum ▁example ▁is ▁ ▁figure ▁D FT - even ▁Hann ▁window , ▁which ▁shows ▁that ▁the ▁- point ▁D FT ▁of ▁the ▁sequence ▁generated ▁by ▁h ann ( ,' period ic ') ▁has ▁only ▁ 3 ▁non - zero ▁values . ▁ ▁All ▁the ▁other ▁samples ▁co inci de ▁with ▁zero - cross ings ▁of ▁the ▁D T FT . ▁ ▁Besides ▁the ▁application ▁already ▁described ▁at ▁# H arm onic ▁analysis , ▁this ▁property ▁is ▁useful ▁for ▁real - time ▁applications ▁that ▁require ▁both ▁window ed ▁and ▁non - window ed ▁( rect angular ly ▁window ed ) ▁transform s , ▁because ▁the ▁window ed ▁transform s ▁can ▁be ▁ ▁efficiently ▁derived ▁from ▁the ▁non - window ed ▁transform s ▁by ▁convolution . ▁ ▁In ▁that ▁application , ▁real - valu ed ▁D FT ▁coefficients ▁( next ▁bullet ) ▁is ▁also ▁an ▁efficiency ▁multip lier . ▁ ▁Real - valu ed ▁D FT ▁coefficients : ▁ ▁Harris ▁( 1 9 7 8 ) ▁c ites ▁this ▁as ▁the ▁D FT ▁equivalent ▁of ▁earlier ▁work , ▁where ▁windows ▁for ▁the ▁D FT ' s ▁prede cess or ▁( finite ▁Fourier ▁transform ) ▁are ▁" always ▁an ▁odd ▁number ▁of ▁points ▁and ▁exhib it ▁even ▁symmetry ▁about ▁the ▁origin ", ▁which ▁results ▁in ▁an ▁entirely ▁real - valu ed ▁D T FT . ▁ ▁The ▁D T FT ▁is ▁a ▁continuous ▁function ▁of ▁frequency ▁ ▁and ▁the ▁D FT ▁is ▁a ▁method ▁of ▁sampling