figured out my mistake
Prove that 1/2 f(t)Dn(x-t)dt = 1/2 f(x-t)Dn(t)dt
the integral ranges from - to
Dn represents the nth Dirichlet's Kernel, e^ikx as k ranges from -n to n
i tried a substitution where u = x - t which yield -du = dt
so the integral i am getting is
1/2 f(t)Dn(x-t)dt = - 1/2 f(x-u)Dn(u)du
any help would be welcomed