▁The ▁custom ary ▁cos ine - sum ▁windows ▁for ▁case ▁K   =   1 ▁have ▁the ▁form : ▁ ▁which ▁is ▁easily ▁( and ▁often ) ▁confused ▁with ▁its ▁zero - phase ▁version : ▁ ▁Setting ▁    ▁produces ▁a ▁Hann ▁window : ▁ ▁named ▁after ▁Julius ▁von ▁Hann , ▁and ▁sometimes ▁referred ▁to ▁as ▁H anning , ▁pres umably ▁due ▁to ▁its ▁lingu istic ▁and ▁formula ic ▁similar ities ▁to ▁the ▁Ham ming ▁window . ▁ ▁It ▁is ▁also ▁known ▁as ▁raised ▁cos ine , ▁because ▁the ▁zero - phase ▁version , ▁ ▁is ▁one ▁lo be ▁of ▁an ▁elev ated ▁cos ine ▁function . ▁ ▁This ▁function ▁is ▁a ▁member ▁of ▁both ▁the ▁cos ine - sum ▁and ▁power - of - s ine ▁families . ▁ ▁Un like ▁the ▁Ham ming ▁window , ▁the ▁end ▁points ▁of ▁the ▁Hann ▁window ▁just ▁touch ▁zero . ▁ ▁The ▁resulting ▁side - lob es ▁roll ▁off ▁at ▁about ▁ 1 8   d B ▁per ▁oct ave . ▁ ▁Setting ▁    ▁to ▁approximately ▁ 0 . 5 4 , ▁or ▁more ▁precisely ▁ 2 5 / 4 6 , ▁produces ▁the ▁Ham ming ▁window , ▁proposed ▁by ▁Richard ▁W . ▁Ham ming . ▁ ▁That ▁choice ▁places ▁a ▁zero - cross ing ▁at ▁frequency ▁ 5 π /( N   −   1 ), ▁which ▁can c els ▁the ▁first ▁s idel obe ▁of ▁the ▁Hann ▁window , ▁giving ▁it ▁a ▁height ▁of ▁about ▁one - fif th ▁that ▁of ▁the