The function f(x) = {1, |x| < 1 0, |x| > 1 is a, symmetrical finite step function.
a) find the fourier sine and cosine transforms for the symmetrical step function f(x) = 1 for |x| < 1 and f(x) = 0 otherwise.
b) from the reult in part a) show that the inverse cosine transform is f(x) = 2 π r [infinity] 0 1 ω sin(ω)cos(ωx)dω.
c) based on the result in b) show that r [infinity] 0 1 ω sin(ω)cos(ωx)dω = π 2 for |x| < 1.