▁window ▁of ▁width ▁. ▁ ▁  ▁▁ ▁At ▁ ▁it ▁becomes ▁rect angular , ▁and ▁at ▁ ▁it ▁becomes ▁a ▁Hann ▁window . ▁ ▁Plan ck - t aper ▁window ▁▁ ▁The ▁so - called ▁" Plan ck - t aper " ▁window ▁is ▁a ▁b ump ▁function ▁that ▁has ▁been ▁widely ▁used ▁in ▁the ▁theory ▁of ▁partitions ▁of ▁unity ▁in ▁manif olds . ▁ ▁It ▁is ▁smooth ▁( a ▁ ▁function ) ▁everywhere , ▁but ▁is ▁exactly ▁zero ▁outside ▁of ▁a ▁compact ▁region , ▁exactly ▁one ▁over ▁an ▁interval ▁within ▁that ▁region , ▁and ▁var ies ▁smooth ly ▁and ▁monot on ically ▁between ▁those ▁limits . ▁ ▁Its ▁use ▁as ▁a ▁window ▁function ▁in ▁signal ▁processing ▁was ▁first ▁suggested ▁in ▁the ▁context ▁of ▁gravit ational - wave ▁astronom y , ▁inspired ▁by ▁the ▁Plan ck ▁distribution . ▁It ▁is ▁defined ▁as ▁a ▁piece wise ▁function : ▁ ▁The ▁amount ▁of ▁tap ering ▁is ▁controlled ▁by ▁the ▁parameter ▁ ε , ▁with ▁smaller ▁values ▁giving ▁sh ar per ▁trans itions . ▁ ▁D P SS ▁or ▁S le p ian ▁window ▁▁ ▁The ▁D P SS ▁( dis crete ▁pro late ▁s ph ero idal ▁sequence ) ▁or ▁S le p ian ▁window ▁maxim izes ▁the ▁energy ▁concentration ▁in ▁the ▁main ▁lo be , ▁and ▁is ▁used ▁in ▁mult it aper ▁spectral ▁analysis , ▁which ▁aver ages ▁out ▁noise ▁in ▁the ▁spectrum ▁and ▁reduces ▁information ▁loss ▁at ▁the ▁edges ▁of ▁the ▁window . ▁ ▁The ▁main ▁lo be ▁ends ▁at ▁a ▁frequency ▁bin