# Thread: Dirichlet's Kernel in Fourier Analysis

1. ## Dirichlet's Kernel in Fourier Analysis

Prove that 1/2$\displaystyle \pi$$\displaystyle \intf(t)Dn(x-t)dt = 1/2\displaystyle \pi$$\displaystyle \int$f(x-t)Dn(t)dt
the integral ranges from -$\displaystyle \pi$ to $\displaystyle \pi$

Dn represents the nth Dirichlet's Kernel, $\displaystyle \sum$ 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$\displaystyle \pi$$\displaystyle \intf(t)Dn(x-t)dt = - 1/2\displaystyle \pi$$\displaystyle \int$f(x-u)Dn(u)du

any help would be welcomed

2. figured out my mistake