▁parameter ▁α ▁sets ▁the ▁Che b ys he v ▁norm ▁of ▁the ▁s idel ob es ▁to ▁− 2 0 α   de ci b els . ▁ ▁The ▁window ▁function ▁can ▁be ▁calculated ▁from ▁W 0 ( k ) ▁by ▁an ▁inverse ▁discrete ▁Fourier ▁transform ▁( DF T ): ▁ ▁The ▁lag ged ▁version ▁of ▁the ▁window ▁can ▁be ▁obtained ▁by : ▁ ▁which ▁for ▁even ▁values ▁of ▁N ▁must ▁be ▁computed ▁as ▁follows : ▁ ▁which ▁is ▁an ▁inverse ▁D FT ▁of ▁  ▁ ▁Vari ations : ▁Due ▁to ▁the ▁equ iri pp le ▁condition , ▁the ▁time - domain ▁window ▁has ▁dis continu ities ▁at ▁the ▁edges . ▁ ▁An ▁approximation ▁that ▁avoid s ▁them , ▁by ▁allowing ▁the ▁equ iri pp les ▁to ▁drop ▁off ▁at ▁the ▁edges , ▁is ▁a ▁Taylor ▁window . ▁An ▁alternative ▁to ▁the ▁inverse ▁D FT ▁definition ▁is ▁also ▁available .. ▁ ▁Ul tras pher ical ▁window ▁▁ ▁The ▁Ul tras pher ical ▁window ▁was ▁introduced ▁in ▁ 1 9 8 4 ▁by ▁Roy ▁Stre it ▁and ▁has ▁application ▁in ▁ ▁anten na ▁array ▁design , ▁non - rec ursive ▁filter ▁design , ▁and ▁spectrum ▁analysis . ▁ ▁Like ▁other ▁adjust able ▁windows , ▁the ▁Ul tras pher ical ▁window ▁has ▁parameters ▁that ▁can ▁be ▁used ▁to ▁control ▁its ▁Fourier ▁transform ▁main - lo be ▁width ▁and ▁relative ▁side - lo be ▁amplitude . ▁Un common ▁to ▁other ▁windows , ▁it ▁has ▁an ▁additional ▁parameter ▁which ▁can ▁be ▁used ▁to ▁set ▁the ▁rate ▁at