▁given ▁by ▁the ▁parameter ▁α . ▁ ▁The ▁Kaiser ▁windows ▁below ▁are ▁created ▁by ▁a ▁simple ▁approximation ▁to ▁the ▁D P SS ▁windows : ▁ ▁Kaiser ▁window ▁▁ ▁The ▁Kaiser , ▁or ▁Kaiser - B essel , ▁window ▁is ▁a ▁simple ▁approximation ▁of ▁the ▁D P SS ▁window ▁using ▁B essel ▁functions , ▁discovered ▁by ▁James ▁Kaiser . ▁▁ ▁  ▁  ▁ ▁where ▁ ▁is ▁the ▁zero - th ▁order ▁modified ▁B essel ▁function ▁of ▁the ▁first ▁kind . ▁ ▁Variable ▁parameter ▁ ▁determ ines ▁the ▁trade off ▁between ▁main ▁lo be ▁width ▁and ▁side ▁lo be ▁levels ▁of ▁the ▁spectral ▁leak age ▁pattern .   ▁ ▁The ▁main ▁lo be ▁width , ▁in ▁between ▁the ▁null s , ▁is ▁given ▁by ▁    ▁in ▁units ▁of ▁D FT ▁b ins ,   ▁and ▁a ▁typical ▁value ▁of ▁ ▁is ▁ 3 . ▁ ▁Dol ph – C heb ys he v ▁window ▁▁ ▁Min im izes ▁the ▁Che b ys he v ▁norm ▁of ▁the ▁side - lob es ▁for ▁a ▁given ▁main ▁lo be ▁width . ▁ ▁The ▁zero - phase ▁Dol ph – C heb ys he v ▁window ▁function ▁ ▁is ▁usually ▁defined ▁in ▁terms ▁of ▁its ▁real - valu ed ▁discrete ▁Fourier ▁transform , ▁: ▁ ▁T n ( x ) ▁is ▁the ▁n - th ▁Che b ys he v ▁polynomial ▁of ▁the ▁first ▁kind ▁evaluated ▁in ▁x , ▁which ▁can ▁be ▁computed ▁using ▁ ▁and ▁ ▁is ▁the ▁unique ▁positive ▁real ▁solution ▁to ▁, ▁where ▁the