ro sc opy ▁with ▁spatial ▁inter fer ometry , ▁is ▁possible ▁by ▁simply ▁subst itut ing ▁a ▁signal ▁with ▁voltage ▁ ▁in ▁equation ▁ ▁to ▁produce ▁the ▁cross - cor relation ▁ ▁and ▁the ▁cross - spect rum ▁. ▁ ▁Example : ▁spatial ▁filtering ▁ ▁In ▁radio ▁astronom y , ▁R F ▁inter ference ▁must ▁be ▁mit ig ated ▁to ▁detect ▁and ▁observe ▁any ▁meaning ful ▁objects ▁and ▁events ▁in ▁the ▁night ▁sky . ▁ ▁Project ing ▁out ▁the ▁inter fer er ▁ ▁For ▁an ▁array ▁of ▁Radio ▁T eles cop es ▁with ▁a ▁spatial ▁signature ▁of ▁the ▁inter fer ing ▁source ▁ ▁that ▁is ▁not ▁a ▁known ▁function ▁of ▁the ▁direction ▁of ▁inter ference ▁and ▁its ▁time ▁variance , ▁the ▁signal ▁cov ar iance ▁matrix ▁takes ▁the ▁form : ▁ ▁where ▁ ▁is ▁the ▁vis ib ilities ▁cov ar iance ▁matrix ▁( s ources ), ▁ ▁is ▁the ▁power ▁of ▁the ▁inter fer er , ▁and ▁ ▁is ▁the ▁noise ▁power , ▁and ▁ ▁denotes ▁the ▁Herm it ian ▁trans pose . ▁One ▁can ▁construct ▁a ▁projection ▁matrix ▁, ▁which , ▁when ▁left ▁and ▁right ▁multip lied ▁by ▁the ▁signal ▁cov ar iance ▁matrix , ▁will ▁reduce ▁the ▁inter ference ▁term ▁to ▁zero . ▁ ▁So ▁the ▁modified ▁signal ▁cov ar iance ▁matrix ▁becomes : ▁ ▁Since ▁ ▁is ▁generally ▁not ▁known , ▁ ▁can ▁be ▁constructed ▁using ▁the ▁eigen - de com position ▁of ▁, ▁in ▁particular ▁the ▁matrix ▁containing ▁an ▁orth on ormal ▁basis ▁of ▁the ▁noise ▁sub space ,