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Construct a periodic system of 4 equations from 8 by adding terms appropriately so that 8 becomes Periodic Array2.doc Wp n W n W n M W n M {1,2,3,4,15,4,3,2} -- note that to keep the array non-singular, that the diagonal element needed to be increased from the original 5. W(-2)=W(-2)+W(2)+W(-6)=3+3=6 W(-1)=W(-1)+W(3)+W(-5)=4+2=6 W(0)=W(0)+W(4)+W(-4) = 15+1 = 16 W(1)=W(1)+W(5)+W(-3)=4+2=6 There is a specific set of frequencies in W representing the location of a very large 1/err 2. We do not want to periodically repeat this. If this location is in the first system, it will be properly represented in the periodic solution.