▁which ▁side - lob es ▁decrease ▁( or ▁increase ) ▁in ▁amplitude . ▁ ▁The ▁window ▁can ▁be ▁expressed ▁in ▁the ▁time - domain ▁as ▁follows : ▁ ▁where ▁ ▁is ▁the ▁Ul tras pher ical ▁polynomial ▁of ▁degree ▁N , ▁and ▁ ▁and ▁ ▁control ▁the ▁side - lo be ▁patterns . ▁ ▁C ertain ▁specific ▁values ▁of ▁ ▁yield ▁other ▁well - known ▁windows : ▁ ▁and ▁ ▁give ▁the ▁Dol ph – C heb ys he v ▁and ▁Sar am ä ki ▁windows ▁respectively . ▁See ▁here ▁for ▁illustr ation ▁of ▁Ul tras pher ical ▁windows ▁with ▁varied ▁paramet riz ation . ▁ ▁Ex pon ential ▁or ▁Po isson ▁window ▁▁ ▁The ▁Po isson ▁window , ▁or ▁more ▁gener ically ▁the ▁exponential ▁window ▁increases ▁expon entially ▁towards ▁the ▁center ▁of ▁the ▁window ▁and ▁decre ases ▁expon entially ▁in ▁the ▁second ▁half . ▁Since ▁the ▁exponential ▁function ▁never ▁reaches ▁zero , ▁the ▁values ▁of ▁the ▁window ▁at ▁its ▁limits ▁are ▁non - zero ▁( it ▁can ▁be ▁seen ▁as ▁the ▁multiplication ▁of ▁an ▁exponential ▁function ▁by ▁a ▁rect angular ▁window ▁). ▁It ▁is ▁defined ▁by ▁ ▁where ▁ τ ▁is ▁the ▁time ▁constant ▁of ▁the ▁function . ▁The ▁exponential ▁function ▁dec ays ▁as ▁e   ≃   2 . 7 1 8 2 8 ▁or ▁approximately ▁ 8 . 6 9   d B ▁per ▁time ▁constant . ▁This ▁means ▁that ▁for ▁a ▁target ed ▁decay ▁of ▁D   d B ▁over ▁half ▁of ▁the ▁window ▁length , ▁the ▁time ▁constant