▁value , ▁whether ▁they ▁are ▁symmetric ▁or ▁asym metric . ▁ ▁Some ▁functions ▁have ▁one ▁or ▁two ▁zero - valu ed ▁end - points , ▁which ▁are ▁unnecessary ▁in ▁most ▁applications . ▁ ▁De let ing ▁a ▁zero - valu ed ▁end - point ▁has ▁no ▁effect ▁on ▁its ▁D T FT ▁( spect ral ▁leak age ). ▁ ▁But ▁the ▁function ▁designed ▁for ▁+ 1 ▁or ▁+ 2 ▁samples , ▁in ▁anticip ation ▁of ▁deleting ▁one ▁or ▁both ▁end ▁points , ▁typically ▁has ▁a ▁slightly ▁nar ro wer ▁main ▁lo be , ▁slightly ▁higher ▁s idel ob es , ▁and ▁a ▁slightly ▁lower ▁noise ▁band width . ▁ ▁D FT - even ▁The ▁termin ology ▁D FT - even ▁( H arr is ▁ 1 9 7 8 , ▁p ▁ 5 2 ) ▁ ▁describes ▁a ▁subclass ▁of ▁periodic ▁( or ▁asym metric ) ▁windows , ▁character ized ▁by ▁only ▁even - length ▁sequences . ▁ ▁Some ▁potential ▁advantages ▁( application - dependent ) ▁for ▁spectral ▁analysis ▁( DF T ) ▁are : ▁ ▁E ffic iency : ▁ ▁F FT ▁algorithms ▁are ▁most ▁efficient ▁when ▁the ▁sequence ▁length ▁is ▁an ▁integer ▁power - of - two . ▁ ▁Zero - valu ed ▁D FT ▁coefficients : ▁ ▁The ▁D FT - even ▁subset ▁of ▁# C os ine - sum ▁windows , ▁including ▁# Rect angular ▁window , ▁have ▁very ▁few ▁non - zero ▁D FT ▁coefficients . ▁ ▁We ▁see ▁the ▁rect angular ▁window ▁effect ▁in ▁the ▁third ▁row