▁ τ ▁is ▁given ▁by ▁ ▁Hy brid ▁windows ▁▁ ▁Window ▁functions ▁have ▁also ▁been ▁constructed ▁as ▁multip lic ative ▁or ▁add itive ▁combinations ▁of ▁other ▁windows . ▁ ▁Bart lett – H ann ▁window ▁ ▁Plan ck – B essel ▁window ▁▁ ▁A ▁# Plan ck - t aper ▁window ▁multip lied ▁by ▁a ▁Kaiser ▁window ▁which ▁is ▁defined ▁in ▁terms ▁of ▁a ▁modified ▁B essel ▁function . ▁This ▁hy brid ▁window ▁function ▁was ▁introduced ▁to ▁decrease ▁the ▁peak ▁side - lo be ▁level ▁of ▁the ▁Plan ck - t aper ▁window ▁while ▁still ▁explo iting ▁its ▁good ▁asympt otic ▁decay . ▁It ▁has ▁two ▁tun able ▁parameters , ▁ ε ▁from ▁the ▁Plan ck - t aper ▁and ▁α ▁from ▁the ▁Kaiser ▁window , ▁so ▁it ▁can ▁be ▁adjust ed ▁to ▁fit ▁the ▁requirements ▁of ▁a ▁given ▁signal . ▁ ▁Hann – Po isson ▁window ▁▁ ▁A ▁Hann ▁window ▁multip lied ▁by ▁a ▁Po isson ▁window , ▁which ▁has ▁no ▁side - lob es , ▁in ▁the ▁sense ▁that ▁its ▁Fourier ▁transform ▁dro ps ▁off ▁forever ▁away ▁from ▁the ▁main ▁lo be . ▁ ▁It ▁can ▁thus ▁be ▁used ▁in ▁hill ▁clim bing ▁algorithms ▁like ▁Newton ' s ▁method . ▁The ▁Hann – Po isson ▁window ▁is ▁defined ▁by : ▁ ▁where ▁α ▁is ▁a ▁parameter ▁that ▁controls ▁the ▁slope ▁of ▁the ▁exponential . ▁ ▁Other ▁windows ▁ ▁Lan cz os ▁window ▁▁▁ ▁used ▁in ▁Lan cz os ▁res am pling ▁ ▁for ▁the ▁Lan cz os ▁window , ▁ ▁is