▁choice ▁for ▁the ▁former ▁and ▁the ▁worst ▁choice ▁for ▁the ▁latter . ▁ ▁What ▁cannot ▁be ▁seen ▁from ▁the ▁graphs ▁is ▁that ▁the ▁rect angular ▁window ▁has ▁the ▁best ▁noise ▁band width , ▁which ▁makes ▁it ▁a ▁good ▁candidate ▁for ▁detect ing ▁low - level ▁sin us oid s ▁in ▁an ▁otherwise ▁white ▁noise ▁environment . ▁ ▁Inter pol ation ▁techniques , ▁such ▁as ▁zero - padding ▁and ▁frequency - sh ifting , ▁are ▁available ▁to ▁mit ig ate ▁its ▁potential ▁scal lop ing ▁loss . ▁ ▁Over la pping ▁windows ▁▁ ▁When ▁the ▁length ▁of ▁a ▁data ▁set ▁to ▁be ▁transformed ▁is ▁larger ▁than ▁necessary ▁to ▁provide ▁the ▁desired ▁frequency ▁resolution , ▁a ▁common ▁practice ▁is ▁to ▁sub div ide ▁it ▁into ▁smaller ▁sets ▁and ▁window ▁them ▁individually . ▁ ▁To ▁mit ig ate ▁the ▁" loss " ▁at ▁the ▁edges ▁of ▁the ▁window , ▁the ▁individual ▁sets ▁may ▁overlap ▁in ▁time . ▁ ▁See ▁Wel ch ▁method ▁of ▁power ▁spectral ▁analysis ▁and ▁the ▁modified ▁discrete ▁cos ine ▁transform . ▁ ▁Two - dimensional ▁windows ▁ ▁Two - dimensional ▁windows ▁are ▁commonly ▁used ▁in ▁image ▁processing ▁to ▁reduce ▁unw anted ▁high - fre qu encies ▁in ▁the ▁image ▁Fourier ▁transform . ▁They ▁can ▁be ▁constructed ▁from ▁one - dimensional ▁windows ▁in ▁either ▁of ▁two ▁forms . ▁The ▁separ able ▁form , ▁ ▁is ▁trivial ▁to ▁compute . ▁The ▁radial ▁form , ▁, ▁which ▁involves ▁the ▁radius ▁, ▁is ▁is otrop ic , ▁independent ▁on ▁the ▁orientation ▁of ▁the ▁coordinate ▁axes . ▁Only