Given the series x, = 2cos(2n .061) + 3 sin(2061), 124 cos(210)+5sin(2r.10r) why does changing the sample size of n=100 to n=128 result in differences between the series when generating a spectral analysis and filtering. The R code to generate the plots are given below (of n 100) x1=2"cosa-p1:100"6/169) +3sina-p11:100.6/100) x24 cos(2*pi 1:1 1/19) 5*sin(2"pi 1:190 1/1S9) x3 6cos(2 pi 1:100 4/10)7 sin(2"pi 1:100 40/190) x =x1+x2 + x3 par(mfrow c(2,2)) plot.ts(x, ylim-e-1,1) main-expressionComega 6/108AA2-13)) plot.ts(x2, ylin-c(-10.10. main-expression(omeg10/16.-A-2-41)) plot.ts(x3, yli c(-19,18), main expressionComega 48/169AA2 85)) plot.tsx. ylis-c-16,16), main-"sum") Hint from the book as follows nWe'll do part of the problem. 12e.aiul" + 1-1.. xit jln Given the series x, = 2cos(2n .061) + 3 sin(2061), 124 cos(210)+5sin(2r.10r) why does changing the sample size of n=100 to n=128 result in differences between the series when generating a spectral analysis and filtering. The R code to generate the plots are given below (of n 100) x1=2"cosa-p1:100"6/169) +3sina-p11:100.6/100) x24 cos(2*pi 1:1 1/19) 5*sin(2"pi 1:190 1/1S9) x3 6cos(2 pi 1:100 4/10)7 sin(2"pi 1:100 40/190) x =x1+x2 + x3 par(mfrow c(2,2)) plot.ts(x, ylim-e-1,1) main-expressionComega 6/108AA2-13)) plot.ts(x2, ylin-c(-10.10. main-expression(omeg10/16.-A-2-41)) plot.ts(x3, yli c(-19,18), main expressionComega 48/169AA2 85)) plot.tsx. ylis-c-16,16), main-"sum") Hint from the book as follows nWe'll do part of the problem. 12e.aiul" + 1-1.. xit jln