  =   1 ), ▁the ▁# Tri angular ▁window ▁( k   =   2 ) ▁and ▁the ▁# Par zen ▁window ▁( k   =   4 ). ▁Altern ative ▁definitions ▁sample ▁the ▁appropriate ▁normal ized ▁B - spl ine ▁basis ▁functions ▁instead ▁of ▁con vol ving ▁discrete - time ▁windows . ▁A ▁k th ▁order ▁B - spl ine ▁basis ▁function ▁is ▁a ▁piece - wise ▁polynomial ▁function ▁of ▁degree ▁k − 1 ▁that ▁is ▁obtained ▁by ▁k - fold ▁self - con volution ▁of ▁the ▁rect angular ▁function . ▁ ▁Tri angular ▁window ▁▁ ▁Tri angular ▁windows ▁are ▁given ▁by : ▁ ▁where ▁L ▁can ▁be ▁N , ▁N + 1 , ▁ ▁or ▁N + 2 .   ▁The ▁first ▁one ▁is ▁also ▁known ▁as ▁Bart lett ▁window ▁or ▁Fe j ér ▁window . ▁ ▁All ▁three ▁definitions ▁conver ge ▁at ▁large ▁N . ▁ ▁The ▁tri angular ▁window ▁is ▁the ▁ 2 nd ▁order ▁B - spl ine ▁window . ▁ ▁The ▁L = N ▁form ▁can ▁be ▁seen ▁as ▁the ▁convolution ▁of ▁two ▁N / 2 ▁width ▁rect angular ▁windows . ▁ ▁The ▁Fourier ▁transform ▁of ▁the ▁result ▁is ▁the ▁squ ared ▁values ▁of ▁the ▁transform ▁of ▁the ▁half - width ▁rect angular ▁window . ▁ ▁Par zen ▁window ▁▁ ▁Def ining ▁  ,   ▁the ▁Par zen ▁window , ▁also ▁known ▁as ▁the ▁de ▁la ▁Vall ée ▁P ous sin ▁window , ▁is ▁the ▁ 4 th ▁order ▁B - spl ine ▁window ▁given ▁by