▁By ▁using ▁Dis crete ▁Fourier ▁Trans form ▁( DF T ) ▁it ▁is ▁possible ▁to ▁analyze ▁signals ▁in ▁the ▁time ▁domain ▁as ▁well ▁as ▁in ▁the ▁spectral ▁domain . ▁The ▁first ▁The ▁first ▁approach ▁is ▁" X F " ▁correlation ▁because ▁it ▁first ▁cross - cor rel ates ▁anten nas ▁( the ▁" X " ▁operation ) ▁using ▁a ▁time - domain ▁" lag " ▁convolution , ▁and ▁then ▁comput es ▁the ▁spectrum ▁( the ▁" F " ▁operation ) ▁for ▁each ▁resulting ▁bas eline . ▁The ▁second ▁approach ▁" FX " ▁takes ▁advantage ▁of ▁the ▁fact ▁that ▁convolution ▁is ▁equivalent ▁to ▁multiplication ▁in ▁Fourier ▁domain . ▁It ▁first ▁comput es ▁the ▁spectrum ▁for ▁each ▁individual ▁anten na ▁( the ▁F ▁operation ), ▁and ▁then ▁multip lies ▁pair wise ▁all ▁anten nas ▁for ▁each ▁spectral ▁channel ▁( the ▁X ▁operation ). ▁A ▁F X ▁correl ator ▁has ▁an ▁advantage ▁over ▁a ▁X F ▁correl ators ▁in ▁that ▁the ▁computational ▁complexity ▁is ▁O ( N 2 ). ▁Therefore , ▁F X ▁correl ators ▁are ▁more ▁efficient ▁for ▁larger ▁arrays . ▁ ▁Cor relation ▁spect rom eters ▁like ▁the ▁Michel son ▁inter fer ometer ▁vary ▁the ▁time ▁lag ▁between ▁signals ▁obtain ▁the ▁power ▁spectrum ▁of ▁input ▁signals . ▁The ▁power ▁spectrum ▁ ▁of ▁a ▁signal ▁is ▁related ▁to ▁its ▁aut oc or relation ▁function ▁by ▁a ▁Fourier ▁transform : ▁ ▁where ▁the ▁aut oc or relation ▁function ▁ ▁for ▁signal ▁X ▁as ▁a ▁function ▁of ▁time ▁delay ▁ ▁is ▁ ▁Cross - cor relation ▁spect