Table 1: Twenty trials which compare the values of the indicated expressions for 𝑀 iterations per trial. The trials are divided into ten trials for two different noise amplitudes. Recall that 𝑀 = 𝑗 . Let 𝑀 = 1 0 0 0 0 and 𝑞 = 0 . 0 0 0 1 .

𝑀 𝑗 = 1 c o s ( 𝑗 𝑞 ) s i n ( 𝑗 𝑞 ) 𝑎 𝑀 𝑗 = 1 c o s ( 𝑗 𝑞 ) s g n ( s i n ( 𝑗 𝑞 ) + 𝑋 𝑗 )

𝑎 = 1
3540.5944043529.425407(1)
3569.469208(2)
3460.5978(3)
3540.394914(4)
3542.955134(5)
3644.993387(6)
3441.978126(7)
3510.495952(8)
3544.098984(9)
3645.64803(10)
𝛽 = 0 . 5 6 4 4 7 % , V a r ( 𝑌 ) = 0 . 8 2 2 9 4 9

𝑎 = 2
3540.5944043578.540737(1)
3468.32837(2)
3063.26568(3)
3629.793227(4)
3562.692845(5)
3605.376332(6)
3284.005063(7)
3375.67384(8)
3356.467161(9)
3500.608956(10)
𝛽 = 1 . 7 3 1 1 5 4 % , V a r ( 𝑌 ) = 0 . 9 5 5 7 3 7