   ▁for ▁  . ▁ ▁General ized ▁normal ▁window ▁ ▁A ▁more ▁generalized ▁version ▁of ▁the ▁Gaussian ▁window ▁is ▁the ▁generalized ▁normal ▁window . ▁Ret aining ▁the ▁notation ▁from ▁the ▁Gaussian ▁window ▁above , ▁we ▁can ▁represent ▁this ▁window ▁as ▁ ▁for ▁any ▁even ▁. ▁At ▁, ▁this ▁is ▁a ▁Gaussian ▁window ▁and ▁as ▁ ▁approaches ▁, ▁this ▁approxim ates ▁to ▁a ▁rect angular ▁window . ▁The ▁Fourier ▁transform ▁of ▁this ▁window ▁does ▁not ▁exist ▁in ▁a ▁closed ▁form ▁for ▁a ▁general ▁. ▁However , ▁it ▁demonstr ates ▁the ▁other ▁benefits ▁of ▁being ▁smooth , ▁adjust able ▁band width . ▁Like ▁the ▁Tu key ▁window ▁discussed ▁later , ▁this ▁window ▁naturally ▁offers ▁a ▁" flat ▁top " ▁to ▁control ▁the ▁amplitude ▁at ten u ation ▁of ▁a ▁time - series ▁( on ▁which ▁we ▁don ' t ▁have ▁a ▁control ▁with ▁Gaussian ▁window ). ▁In ▁ess ence , ▁it ▁offers ▁a ▁good ▁( cont roll able ) ▁comprom ise , ▁in ▁terms ▁of ▁spectral ▁leak age , ▁frequency ▁resolution ▁and ▁amplitude ▁at ten u ation , ▁between ▁the ▁Gaussian ▁window ▁and ▁the ▁rect angular ▁window . ▁See ▁also ▁ ▁for ▁a ▁study ▁on ▁time - fre quency ▁representation ▁of ▁this ▁window ▁( or ▁function ). ▁ ▁Tu key ▁window ▁▁ ▁Def ining ▁  ,   ▁the ▁Tu key ▁window , ▁also ▁known ▁as ▁the ▁cos ine - t aper ed ▁window , ▁can ▁be ▁regarded ▁as ▁a ▁cos ine ▁lo be ▁of ▁width ▁ ▁that ▁is ▁con vol ved ▁with ▁a ▁rect angular